Propagation Of Solitary Waves Research Articles

Mixed neural operator learning on the solitary wave propagation over slope topography and inverse problem

This study proposes the mixed neural operator (MNO) learning framework, which further combines with the particle swarm optimization (PSO) to address challenges of solitary wave propagation over topography. The forward problem is defined as the evolution prediction of the solitary wave propagating over topography, while the inverse problem is defined as an optimization to identify the topography parameter based on the solitary wave elevation. Both the forward and inverse problems can be considered within a single framework and the dataset are provided by the classical Korteweg–de Vries (KdV) equation. The MNO framework is shown to simulate the evolution of solitary waves over topography, accurately capturing the wave elevation under different topographical conditions. By comparing with different neural operators, it is found that the U-shape neural operator is the most suitable for the KdV equation simulation. The coefficient of determination for the inverse problem based on the combination of MNO and PSO can reach 0.992, showing great potential of the approach in topography recognition. Finally, the proposed learning framework is preliminary applied to the prediction of the tsunami runup onto a complex beach, and a good agreement is also achieved between the direct simulation and the learning framework prediction.

Oblique propagation of dust acoustic solitary waves in a magnetized plasma in the presence of cairns-tsallis distributed ions

We investigate the effects of non-extensivity (q), non-thermality (α), obliqueness (l z ), the strength of the magnetic field (ω c ), and dust grain temperature (σ d ) on the basic features (viz., amplitude, width, velocity, and soliton energy) of obliquely propagating dust-acoustic solitary waves (DASWs) in a magnetized dusty plasma, which consists of highly negatively charged dust grains, Boltzmann-distributed electrons, and nonthermal non-extensive Cairns-Tsallis(C-T)-distributed ions. First, we derived the expression of the C-T polarization force and analyzed the combined effects of the ions’ non-extensivity (q) and non-thermality (α) parameters on the magnitude (R) of this polarization force. Our results show that R strongly depends on both the q-parameter and the α-parameter. Specifically, for q < 1, the ions’ non-extensivity and non-thermality weaken the polarization force, whereas for q > 1, R shifts toward higher values. Thus, the obliquely propagating DASWs are more likely to form in a magnetized non-extensive plasma rather than in a magnetized extensive plasma q = 1. Subsequent key findings are as follows: The wave phase velocity increases linearly as the obliquity (l z ) decreases. This implies that a reduced obliqueness results in faster soliton motion and spikier solitary structures. Moreover, the amplitude (width) of DASWs decreases (increases) with increasing l z . An increase in the magnetic field magnitude (ω c ) affects only the width of the DASWs. The amplitude (width) of DASWs decreases (increases) with higher dust grain temperature (σ d ). This indicates that dust temperature significantly affects wave excitation. Specifically, at higher dust temperatures, dispersion dominates over nonlinear effects, resulting in smoother solitary structures. The soliton’s energy increases with α and becomes more pronounced as q decreases (from 1 to 0.75). It increases also with higher ω c and dust temperature (σ d ), especially in the presence of nonthermal energetic particles. This investigation provides valuable insights into the propagation mechanisms of nonlinear DASWs in both space and laboratory plasmas containing non-extensive, nonthermal C-T-distributed ions and dust grains.

Development of a smoothed particle hydrodynamics model for porous media flows with enhanced volume conservation and the revisit of the mass conservation equation

Porous media exist extensively in hydraulic and coastal engineering structures, while the modeling of wave/flow interaction with porous media remains challenging. This work develops a smoothed particle hydrodynamics (SPH) model for accurately simulating wave/flow interaction with porous media. The mass and momentum conservation equations incorporating the mixture theory are adopted. The resistant forces of the solid skeleton of porous media on fluid flows are described by the nonlinear empirical formula. The research contributions of the work lie in two aspects. First, two categories of mass conservation equations for porous media flow are revisited and analyzed to examine the influences of the local time derivative term of fluid volume fraction on simulation results. Second, the Volume Conservation Shifting scheme is, for the first time, introduced into SPH to enhance volume conservation for simulating porous media flows. The developed SPH model is validated by an analytical case of seepage flows in a U-tube with porous media and then applied to study four benchmark examples involving both saturated and unsaturated porous media, i.e., dam-break flow through a crushed stone dam, rapid seepage flow through a rockfill dam, solitary wave propagation over a porous seabed, and solitary wave propagation over a submerged porous breakwater. The morphological features and dynamic pressure heads of the porous media flows have been satisfactorily predicted, demonstrating the good accuracy and enhanced volume conservation of the developed SPH model.

The effect of dust on the propagation of a hydromagnetic solitary wave along the magnetic field in a cold collision-free plasma

The effect of dust is studied on the parallel propagation of a solitary hydromagnetic wave in a magnetized, cold, collision-free plasma. The fully nonlinear analysis is based on the Adlam–Allen method. The system of nonlinear differential equations was derived using the assumption of massive dust, namely, that the dust velocity is constant and parallel to the background magnetic field. Self-consistent solutions obtained from the model for the lighter particles dynamics and for the resulting electric and magnetic fields are presented, together with the validity range of Mach numbers as a function of dust parameters. In particular, supersonic solutions are possible in scenarios tending to two-component plasmas (positively charged ions and negatively charged dust). The stationary solitary pulse in terms of particle densities, magnitude of transverse magnetic field, transverse electron–ion velocities, and bipolar electric field is presented. The magnitude of these amplitudes is maximum at the center of wave and minimum at the boundary. Furthermore, it is shown that all the solitary wave amplitudes are decreases with dust parameter.

A Weierstrass approach to the analysis of rarefaction solitary waves in tensegrity mass-spring systems

Abstract The Weierstrass‘ theory of one-dimensional Lagrangian systems and a quasi-continuum approach are employed to study the propagation of solitary waves in tensegrity mass-spring chains, which exhibit softening-type elastic response in the large displacement regime and are subject to external pre-compression. The presented study analytically derives the shape of the traveling rarefaction pulses, and limiting values of the speeds of such pulses. Use is made of a tensegrity-like interaction potential that captures the main features of the real force-displacement response of the examined units. The Weierstrass approach is validated through numerical applications that establish comparisons between the theory developed in the present work and previous results available in literature.

Generation of Solitary Waves with Analytical Solution for The (3+1)-dimensional pKP-BKP Equation and Reductions

In this study, new solitary wave solutions are obtained for the combination of the B-type Kadomtsev-Petviashvili (BKP) equation and the potential Kadomtsev-Petviashvili (pKP) equation, called the integrable (3+1)-dimensional coupled pKP-BKP equation, and its two reduced forms. For this purpose, the Bernoulli auxiliary equation method, which is an ansatz-based method, is used. As a result, kink, lump, bright soliton and breather wave solutions are observed. It is concluded that this method and the results obtained for the considered pKP -BKP equations are an important step for further studies in this field.

Multi-dimensional modeling of solitary wave–structure interaction problems by using a [formula omitted]-LES-SPH model

The interaction mechanisms between waves and marine structures are a popular research topic. This paper applies the weakly compressible smoothed particle hydrodynamics (WCSPH) method to study the dynamics of green water overtopping. To enhance the accuracy of the simulations, the SPH method coupled with the large eddy simulation (LES) model is employed for numerical investigations. Initially, we validate the effectiveness of the model by simulating the generation of solitary waves and irregular waves, as well as numerically reproducing the water surface morphology during the interaction between solitary waves and the deck. Subsequently, the validated model is used to study the dynamic characteristics of different types of waves overtopping, revealing significant variations in their motion. Furthermore, we investigate the effect of deck roughness during the entire green water overtopping process in terms of both protrusions extent and distribution, confirming that a reasonable setting of the protrusions can greatly reduce the wave impact loads on the deck, thereby protecting the structure. Additionally, a three-dimensional model is developed to study the green water problem, and we find that the turbulence phenomenon is more pronounced in the three-dimensional scenario.

Nonlinear dust ion acoustic solitary waves propagation in a magnetized plasma with Tsallis electron distribution

Abstract We have done a theoretical investigation into the propagation of nonlinear dust ion acoustic solitary waves and their soliton properties in a three-component magnetized collisionless plasma consisting of inertial positively charged ions, noninertial electrons following a Tsallis q–distribution, and stationary negatively charged dust grains. We consider a uniform external magnetic field along the z–direction, and the wave propagation occurs obliquely to the magnetic field direction. It is observed that the two types of wave modes namely slow and fast modes, are appears in the linear analysis. By employing the reductive perturbation method, the Korteweg-de Vries (KdV) and modified KdV equations are determined to describe the small amplitude dust ion acoustic soliton. The dependence of several physical plasma parameters including nonextensive q–parameter, magnetic field strength etc. of our plasma on the propagating dust ion acoustic solitary waves potential are numerically examined. This study shows the simultaneous existence of compressive and rarefactive solitons due to the variation of first order nonlinearity coefficient represented by the KdV equation and it is found that there is a critical point for the plasma parameters where the amplitude of the soliton of KdV equation become diverges. The mKdV equation with second order nonlinearity coefficient is derived from there and observed the solitons only with finite amplitude. The present study could be helpful for understanding the nonlinear travelling waves propagating in laboratory and space plasma environments.

Nonlinear waves for a variable-coefficient modified Kadomtsev-Petviashvili system in plasma physics and electrodynamics

Abstract In this paper, a variable-coefficient modified Kadomtsev-Petviashvili (vcmKP) system is investigated modeling the propagation of electromagnetic wave in an isotropic charge-free infinite ferromagnetic thin film and nonlinear waves in plasma physics and electrodynamics. Painlevé analysis is given out, and an auto-Bäcklund transformation is constructed via the truncated Painlevé expansion. Based on the auto-Bäcklund transformation, analytic solutions are given, including the solitonic, periodic and rational solutions. Using the Lie symmetry approach, infinitesimal generators and symmetry groups are presented. With the Lagrangian, the vcmKP equation is shown to be nonlinearly self-adjoint. Moreover, conservation laws for the vcmKP equation are derived by means of a general conservation theorem. Besides, the physical characteristics of the influences of the coefficient parameters on the solutions are discussed graphically. Those solutions have comprehensive implications for the propagation of solitary waves in the nonuniform backgrounds.

A numerical model for solitary wave breaking based on the phase-field lattice Boltzmann method

This study presents a numerical investigation of a solitary wave breaking over a slope by using the phase-field lattice Boltzmann method. The incompressible two-phase flow equations are solved by using a velocity-based formulation of the two-phase lattice Boltzmann method with a central-moment collision model to accurately simulate wave breaking problems. For interface capture, a phase-field lattice Boltzmann method that ensures mass conservation is employed. The validity of the proposed method is confirmed through solitary wave propagation and transformation problems, and the obtained results are in good agreement with the experimental and calculated results. The proposed method is then employed to analyze wave breaking on a slope, demonstrating strong concordance with experimental data and existing computational findings. By analyzing the instantaneous flow characteristics and the temporal evolution of the variation in kinetic, potential, and total energy from deep to shallow water, the model can reveal the macroscopic characteristics of solitary wave breaking. Because the phase-field model effectively simulates wave breaking and air entrainment, it can depict wave energy dissipation more accurately than the single-phase lattice Boltzmann method with free surface tracking.

Analysis of fractional solitary wave propagation with parametric effects and qualitative analysis of the modified Korteweg-de Vries-Kadomtsev-Petviashvili equation

This study explores the fractional form of modified Korteweg-de Vries-Kadomtsev-Petviashvili equation. This equation offers the physical description of how waves propagate and explains how nonlinearity and dispersion may lead to complex and fascinating wave phenomena arising in the diversity of fields like optical fibers, fluid dynamics, plasma waves, and shallow water waves. A variety of solutions in different shapes like bright, dark, singular, and combo solitary wave solutions have been extracted. Two recently developed integration tools known as generalized Arnous method and enhanced modified extended tanh-expansion method have been applied to secure the wave structures. Moreover, the physical significance of obtained solutions is meticulously analyzed by presenting a variety of graphs that illustrate the behaviour of the solutions for specific parameter values and a comprehensive investigation into the influence of the nonlinear parameter on the propagation of the solitary wave have been observed. Further, the governing equation is discussed for the qualitative analysis by the assistance of the Galilean transformation. Chaotic behavior is investigated by introducing a perturbed term in the dynamical system and presenting various analyses, including Poincare maps, time series, 2-dimensional 3-dimensional phase portraits. Moreover, chaotic attractor and sensitivity analysis are also observed. Our findings affirm the reliability of the applied techniques and suggest its potential application in future endeavours to uncover diverse and novel soliton solutions for other nonlinear evolution equations encountered in the realms of mathematical physics and engineering.

Shear Bands Triggered by Solitary Porosity Waves in Deforming Fluid‐Saturated Porous Media

AbstractThe interplay between compaction‐driven fluid flow and plastic yielding within porous media is investigated through numerical modeling. We establish a framework for understanding the dynamics of fluid flow in deforming porous materials that corresponds to the equations describing solitary porosity wave propagation. A concise derivation of the coupled fluid flow and poro‐viscoelastoplastic matrix behavior is presented, revealing a connection to Biot's equations of poroelasticity and Gassmann's theory in the elastic limit. Our findings demonstrate that fluid overpressure resulting from channelized fluid flow initiates the formation of new shear zones. Through three‐dimensional simulations, we observe that the newly formed shear zones exhibit a parabolic shape. Furthermore, plasticity exerts a significant influence on both the velocity of fluid flow and the shape of fluid channels. Importantly, our study highlights the potential of spontaneous channeling of porous fluids to trigger seismic events by activating both new and pre‐existing faults.

2DH Numerical Study of Solitary Wave Processes around an Idealized Reef-Fringed Island

In order to better understand the role of coral reefs around an isolated island in mitigating tsunami hazards, this study performed a horizontally two-dimensional (2DH) numerical study of tsunami-like solitary wave propagation and run-up around an idealized reef-fringed island. The shock-capturing Boussinesq wave model, the FUNWAVE-TVD is used in the present study and well-validated with existing experimental data for its robustness in predicting 2DH solitary wave processes around an island. Based on the validated model, the typical solitary propagation process around the reef-fringed island and the effects of morphological and hydrodynamic parameters on the maximum run-up heights were systematically investigated. It is found that coral reefs can effectively reduce maximum run-up heights around an isolated island. The reef flat’s water depth, reef flat width, and reef surface roughness are the main factors affecting maximum run-up heights around an island, while the fore-reef slope has little impact. For the idealized reef-fringed island in this study, sea-level rise will cause coral reefs to lose their protective capability on the lee side, and the presence of coral reefs may even enhance tsunami hazards around an island when the reef flat width is very narrow or coral bleaching happens.

Large-amplitude internal waves and turbulent mixing in three-layer flows under a rigid lid

We consider a nonlinear long-wave Boussinesq-type model describing the propagation of breaking internal solitary waves in a three-layer flow between two rigid boundaries. The Green–Naghdi-type equations govern the fluid flow in the top and bottom homogeneous layers. In the intermediate hydrostatic layer, the fluid is non-homogeneous, and its flow is described by the depth-averaged shallow water equations for shear flows. The velocity shear in the outer layers can lead to the development of the Kelvin–Helmholtz instability and turbulent mixing. To take this into account, we propose a simple law of vertical mixing, which governs the interaction of these layers. Stationary solutions and non-stationary calculations show the effect of mixing (or breaking) for waves of sufficiently large amplitude. We construct steady-state soliton-like solutions of the three-layer model adjacent to a given constant flow. The obtained theoretical profiles of breaking solitary waves are consistent with laboratory experiments.

Nonplanar ion acoustic waves in e-p-i plasmas with non-Maxwellian distributed electrons and positrons

The process of propagation of cylindrical and spherical ion acoustic solitary waves in an electron, positron, and ion plasma system is studied. The electrons are considered to have the generalized (r, q) distribution, while the positrons are supposed to have the kappa distribution, also known as the Lorentzian distribution. The classic nonlinear equation, Korteweg de-Vries (KdV), has been numerically solved by employing appropriate mathematical transformations. The role of various plasma parameters and nonplanar geometry on the widths and amplitudes of nonlinear ion acoustic structures has been numerically investigated. The current study could be helpful to understand the significance of cylindrical and spherical solitary waves in laboratory, astrophysical as well as in space plasmas.

Physics-informed neural networks for fully non-linear free surface wave propagation

This study proposed fully nonlinear free surface physics-informed neural networks (FNFS-PINNs), an advancement within the framework of PINNs, to tackle wave propagation in fully nonlinear potential flows with the free surface. Utilizing the nonlinear fitting capabilities of neural networks, FNFS-PINNs offer an approach to addressing the complexities of modeling nonlinear free surface flows, broadening the scope for applying PINNs to various wave propagation scenarios. The improved quasi-σ coordinate transformation and dimensionless formulation of the basic equations are adopted to transform the time-dependent computational domain into the stationary one and align variable scale changes across different dimensions, respectively. These innovations, alongside a specialized network structure and a two-stage optimization process, enhance the mathematical formulation of nonlinear water waves and solvability of the model. FNFS-PINNs are evaluated through three scenarios: solitary wave propagation featuring nonlinearity, regular wave propagation under high dispersion, and an inverse problem of nonlinear free surface flow focusing on the back-calculation of an initial state from its later state. These tests demonstrate the capability of FNFS-PINNs to compute the propagation of solitary and regular waves in the vertical two-dimensional scenarios. While focusing on two-dimensional wave propagation, this study lays the groundwork for extending FNFS-PINNs to other free surface flows and highlights their potential in solving inverse problems.

The modified cubic Benjamin–Ono equation describing internal solitary waves in the deep ocean and its related properties

In this article, we investigate the propagation of internal solitary waves in deep ocean. Based on the principles of nonlinear theory, perturbation expansion, and multi-scale analysis, a time-dependent modified cubic Benjamin–Ono (mCBO) equation is derived to describe internal solitary waves in the deep ocean with stronger nonlinearity. When the dispersive term ∂3f∂X3 vanishes, the mCBO equation transforms into the cubic BO equation. Similarly, when the dispersive term ∂3f∂X3 becomes zero and the nonlinear term ∂f3∂X degenerates into ∂f2∂X, the mCBO equation reduces to the BO equation. Furthermore, if the integral term ∂2∂X2ℵ(f) disappears, it simplifies to the mKdV equation. To gain deeper insight into the characteristics of solitary waves, conservation of mass and momentum associated with them are discussed. By employing Hirota's bilinear method, we obtain soliton solutions for the mCBO equation and subsequently investigate interactions between two solitary waves with different directions, leading to the occurrence of important events such as rogue waves and Mach reflections. Additionally, we explore how certain parameters influence Mach stem while drawing meaningful conclusions. Our discoveries reveal the complex dynamics of internal solitary waves within the deep ocean and contribute to a broader understanding of nonlinear wave phenomena.

On the transverse stability of smooth solitary waves in a two-dimensional Camassa–Holm equation

We consider the propagation of smooth solitary waves in a two-dimensional generalization of the Camassa–Holm equation. We show that transverse perturbations to one-dimensional solitary waves behave similarly to the KP-II theory. This conclusion follows from our two main results: (i) the double eigenvalue of the linearized equations related to the translational symmetry breaks under a transverse perturbation into a pair of the asymptotically stable resonances and (ii) small-amplitude solitary waves are linearly stable with respect to transverse perturbations.

Ion acoustic solitary waves in an adiabatic dusty plasma: Roles of superthermal electrons, ion loss and ionization

Abstract The propagation of dust ion acoustic solitary wave (DIASW) is investigated in the multicomponent dusty plasma with adiabatic ions, superthermal electrons and stationary dust. The reductive perturbation method is employed to derive the damped Korteweg-de Vries (DKdV) equation which describes DIASW. The result reveals that, the adiabaticity of ions significantly modifies the basic features of the DIASW. The ionization effect makes the solitary wave growing, while collisions reduce the growth rate and even lead to the damping. With the increase in ionization cross section $\frac{{\Delta \sigma }}{{{\sigma _0}}}$, ion-to-electron density ratio ${{\delta}_{\rm{ie}}}$ and superthermal electrons parameter $\kappa $, the effect of ionization on DIASW enhances.

Generation of diurnal internal solitary waves (ISW-D) in the Sulu Sea: From geostationary orbit satellites and numerical simulations

Our recent study reported the existence of internal solitary waves with the diurnal tidal cycle (ISW-D) in the Sulu Sea, however, the three-dimensional characteristics and generation mechanism of ISW-D are still unclear (Huang et al., 2023). In this work, the spatial–temporal characteristics, generation mechanism and propagating process of ISW-D in the Sulu Sea are first preliminary investigated based on high-temporal-resolution Geostationary Orbiting Satellite (GOS) images and high-spatial-resolution two-dimensional numerical model (MITgcm). GOS images from 2018-2022 are retrieved and a total of 13 pairs of ISW-D packets are found. ISW-D occur at spring tide during May–August, with an average interpacket distance of 198 km and a phase speed of 2.30 m/s. To further knowledge of the generation mechanism and propagation process of ISW-D, the non-linear and non-hydrostatic numerical simulations are conducted. The comparison of ISW-D parameters with GOS images proves the validity of numerical simulations. The results of numerical simulations and theoretical parameters indicate that ISW-D are generated at the sill near Pearl Bank by internal tide release mechanism. Moreover, three sensitivity experiments are designed to investigate the effects of tidal force and seawater stratification on the generation and propagation of ISW-D. The results reveal that the ISW-D is generated by diurnal tides with stronger intensity than semidiurnal tides. Seawater stratification does not influence the generation of ISW-D but modulates the propagation process. Phase speeds from GOS images and theoretical model show a positive correlation between the phase speeds of ISW-D and the intensity of seawater stratification.