Behavior Of Solitary Waves Research Articles

Internal Solitary Waves in the Andaman Sea Revealed by Long-Term Mooring Observations

AbstractThe complex behaviors of internal solitary waves (ISWs) in the Andaman Sea were revealed using data collected over a nearly 22-month-long observation period completed by two moorings. Emanating from the submarine ridges northwest of Sumatra Island and south of Car Nicobar, two types of ISWs, referred to as S- and C-ISWs, respectively, were identified in the measurements, and S-ISWs were generally found to be stronger than C-ISWs. The observed S- and C-ISWs frequently appeared as multiwave packets, accounting for 87% and 43% of their observed episodes, respectively. The simultaneous measurements collected by the two moorings featured evident variability along the S-ISW crests, with the average wave amplitude in the northern portion being 36% larger than that in the southern portion. The analyses of the arrival times revealed that the S-ISWs in the northern portion occurred more frequently and arrived more irregularly than those in the southern portion. Moreover, the temporal variability of ISWs drastically differed on monthly and seasonal time scales, characterized by relatively stronger S-ISWs in spring and autumn. Over the interannual time scale, the temporal variations in ISWs were generally subtle. The monthly-to-annual variations of ISWs could be mostly explained by the variability in stratification, which could be modulated by the monsoons, the winds in equatorial Indian Ocean, and the mesoscale eddies in the Andaman Sea. From careful analyses preformed based on the long-term measurements, we argued that the observed ISWs were likely generated via internal tide release mechanism and their generation processes were obviously modulated by background circulations.

Investigation of shallow water waves and solitary waves to the conformable 3D-WBBM model by an analytical method

In this article, we elucidate the dynamical behavior of exact solitary waves to the conformable 3D Wazwaz-Benjamin- Bona-Mahony (3D-WBBM) equation emerging in shallow water waves. A variety of nonlinear dynamical solitary wave structures are extracted in different shapes like hyperbolic, trigonometric, and exponential function solutions including some special known solitary wave solution like bell shaped, shock, singular and multiple soliton by an analytical mathematical tool namely the generalized exponential rational function method (GERFM). Besides, we also secure singular periodic wave solutions with unknown parameters. All the secured solutions are verified by substituting back to the original equation through soft computation Mathematica. The outcomes show that the governing model theoretically possesses extremely rich structures of exact solitary wave solutions. The physical characterization of some reported results are figured out graphically in 3D, 2D and their corresponding contour profiles by selecting appropriate values of parameters.

Behavior of solitary waves of coupled nonlinear Schrödinger equations subjected to complex external periodic potentials with odd- symmetry

We discuss the response of both moving and trapped solitary wave solutions of a two-component nonlinear Schrödinger system in 1 + 1 dimensions to an odd- external periodic complex potential. The dynamical behavior of perturbed solitary waves is explored by conducting numerical simulations of the nonlinear system and using a collective coordinate variational approximation. We present case examples corresponding to choices of parameter values and initial conditions involved therein. The results of the collective coordinate approximation are compared against numerical simulations where we observe qualitatively good agreement between the two. Unlike the case for a single-component solitary wave in a complex periodic -symmetric potential, the collective coordinate equations do not have a small oscillation regime, and initially the height of the two components changes in opposite directions often causing instability. We find that the dynamic stability criteria we have used in the one-component case are a good indicator for the onset of dynamic instabilities in the present setup.

Theoretical and experimental investigation on strongly nonlinear internal solitary waves moving over slope-shelf topography

The variable-coefficient modified Gardner equation is proposed to describe large amplitude internal solitary waves (ISWs) propagating over slope-shelf topography. The model is adapted from weakly nonlinear Gardner equation by adjusting its original coefficients such that the model is capable of representing the crucial characteristics of large amplitude ISWs, including the effective wavelength and wave speed. To numerically solve the nonlinear equation, the fourth-order Runge-Kutta method is applied for temporal discretization, second-order central finite difference numerical scheme is implemented for the space discretization and the iterative scheme is applied to treat the coupling term of time and space. The numerical method is then verified by comparing fairly with laboratory experiments. It's found the variable-coefficient modified Gardner model is a reliable theoretical tool to describe the behavior of large amplitude internal solitary waves passing through bottom topography.

Bifurcation of gap solitary waves in a two-dimensional electrical network with nonlinear dispersion

Abstract In this paper, the behavior of gap solitary waves is investigated in a two-dimensional electrical line with nonlinear dispersion. Applying the semidiscrete approximation, we show that the dynamics of modulated wave in the network can be described by an extended nonlinear Schrodinger equation. With the aid of the dynamical systems approach, we examine the fixed points of our model equation and the bifurcations of its phase portrait are presented. Likewise, we derive the exact parametric representations of bright soliton, dark soliton, peak and anti-peak solitons, kink and anti-kink solitons, periodic solutions and some compacton solutions corresponding to the various phase portrait trajectories under different parameter conditions. We find out that the nonlinear dispersion considerably affects the dynamics of the system and leads to a number of new solitary-wave solutions, namely, peakon, periodic peakon, compacton solutions, which can not be observed when the dispersion is assumed linear.

Study of Dust-Acoustic Multisoliton Interactions in Strongly Coupled Dusty Plasmas

The effect of the structure parameter on the compressibility of dust grains and soliton behavior in a dusty plasma system consisting of Maxwellian electrons, ions, and dust grains charged with a negative charge has been studied. In the theoretical study, a reductive perturbation technique was used to derive the Korteweg-de Vries (KdV) equation and employ the Hirota bilinear method to obtain multisoliton solution. It is found that coupling and structure parameters have a clear effect on the compressibility. These changes in the compressibility affected the amplitude and width of interactive solitons, in addition to the phase shifts resulting from the interaction. These results can be used to understand the behavior of solitary waves that occur in various natural and laboratory plasma environments with dust impurity situations.

Dust ion acoustic solitons in a complex dusty plasma system with an adiabatic state

In this theoretical work nonlinear behavior of dust ion acoustic solitary waves (SWs) has been investigated, and then the effect of the adiabatic change on them has been observed. The complex plasma system consists of inertial positive and negative ions, Maxwell's electrons, and positively and negatively charged stationary dust particles. The effects of dust polarity on the dust ion acoustic SWs have also been observed. Using the reductive perturbation method, we first derive K-dV equation which lets to analyze both the positive (bright) and negative (dark) solitons in a very limited region. After that mK-dV equation has been derived, and this let to analyze positive soliton for a large region, but cannot show the negative soliton. Finally, the Gardner equation has been derived employing the same method, through which we were able to analyze both the positive and negative solitons for a large region. It has been found that both the positive and negative solitons significantly depend on the mass number density, ion number density, and dust polarity in the adiabatic and isothermal system.

Generalized nonlinear Schrödinger equation: Conservation of energy and solitary-wave solutions

We show the conservation of momentum and energy of a generalized nonlinear Schrödinger equation. Moreover, we obtain a new traveling-wave solution of this equation with an additional term of the form Γ(ψ(x, t)) = λ1ψ(x, t) + λ2ψ(x,t)q + λ3ψ(x,t)2−2q. We present two cases where the density of energy of the system, for the traveling-wave solution, has a solitary-wave behavior.

Integral complex modified Korteweg-de Vries (Icm-KdV) equations

Abstract In this article we examine different ways of introducing nonlocal effects in the complex modified Korteweg-de Vries (cmKdV) equation. Four possible nonlocal generalizations of the cmKdV equation are presented. In these variants of the cmKdV equation the nonlinear term has been replaced by one, two, or three integral terms. Three of these variants can be obtained by the least action principle, and they possess different equivalent Lagrangians. The relationship between these Lagrangians is entirely new. Therefore, a novel type of Lagrangian equivalence has been found. As Fubini´s theorem is needed to prove the equivalence of these Lagrangians, we call them “F-equivalent”. Noether´s theorem is applied to these integral equations, and different conserved quantities are obtained. The behavior of solitary waves in these models is also studied. It was found that one of these models has soliton-like solutions. Numerical solutions show that these solitons are stable, and the amplitudes of perturbed solitons attain constant values after a short transient period. Finally, a variational method was applied to get a better understanding of the behavior of these pulses during the transient periods.

Numerical simulation of solitary waves overtopping on a sloping sea dike using a particle method

Sea dikes, as a commonly used type of coastal protection structures, are often attacked or damaged by violent waves overtopping under tsunamis and storm surges. In this study, the behavior of solitary waves traveling on a sloping sea dike is simulated, and solitary wave overtopping characteristics are analyzed using a complete Lagrangian numerical method, the moving particle semi-implicit (MPS) method. To better describe the complicated fluid motions during the wave overtopping process, the original MPS method is modified by introducing a new free surface detection method, i.e., the area filling rate identification method, and a modified gradient operator to provide higher precision. Meanwhile, the approximation method for sloping boundaries in particle methods is enhanced, and a smooth slope approximation method is proposed and recommended. To verify the improved MPS method, a solitary wave traveling over a steep sloping bed is studied. The entire solitary wave run-up and run-down processes and exquisite water movements are reproduced well by the present method, and are consistent with the corresponding experimental results. Subsequently, the improved MPS method is applied to investigate the overtopping process of a single solitary wave over a sloping sea dike. The results show that the hydraulic jump phenomenon is also possible to occur during the run-down motion of the solitary wave overtopping. Finally, the characteristics of the propagation and overtopping of two successive solitary waves on a sloping sea dike are discussed. The result manifests that the interaction between adjacent solitary waves affects wave overtopping patterns and overtopping velocities.

Behavior of Electron Acoustic Solitary Waves in an Unmagnetized Quantum Plasma Containing Two-Temperature Electrons

Behavior of Electron Acoustic Solitary Waves in an Unmagnetized Quantum Plasma Containing Two-Temperature Electrons

Shock wave generation in plasmas at varying magnetic field

By considering the continuity, the Navier-Stokes and Poisson's equations in a nonrelativistic framework for plasmas, we study the behavior of small amplitude ion acoustic solitary waves in plasmas under the influence of a varying magnetic field. The result is a nonlinear wave equation which complies with the modified Korteweg-de Vries-Burgers equation, surprisingly in the absence of thermal pressure or any dissipative effects. We show that the complete set of equations, by considering the varying magnetic field, creates solitary waves which radiate energy during their travel in the medium. An interesting result is the existence of small amplitude localized shock profiles beside the solitary waves. Properties of this solitaire solution are studied by considering different values for the environmental characters.

Long-time behavior of three-dimensional gravity-capillary solitary waves on deep water generated by a moving air-blowing forcing: Numerical study

Long-time behavior of three-dimensional gravity-capillary solitary waves on deep water generated by a moving air-blowing forcing: Numerical study

Structure of equatorial envelope Rossby solitary waves with complete Coriolis force and the external source

In this article, the behavior of the equatorial envelope Rossby solitary waves with complete Coriolis force and the external source are investigated analytically. By the asymptotic method of multiple scales and perturbation expansions, a new cubic nonlinear Schrödinger equation with complete Coriolis force and the external source is derived to describe the evolution of equatorial envelope Rossby solitary waves. The equation is different from the common Schrödinger equation, it is more suitable for describing envelope Rossby solitary waves when the horizontal component Coriolis force is stronger near the equator. Using the equation, the features of generalized beta, the horizontal component of Coriolis force and the external source are presented. And then various periodic structures for equatorial envelope Rossby solitary waves are obtained with the help of Jacobi elliptic functions and elliptic equation. Particularly, the solution of envelope Rossby solitary waves is obtained and graphical presentations are shown for Rossby solitary waves amplitude with the different Coriolis parameters. It is pointed out that with decreasing of Coriolis parameter λ, the amplitude of Rossby solitary waves decreases, whereas the propagating frequency is unchanged. And we find that the periodic solution of the nonlinear Schrödinger equation have different structures with a phase-locked diabatic heating source and without a source.

Dynamics of the breather waves, rogue waves and solitary waves in an extend Kadomtsev–Petviashvili equation

Under investigation in this work is an extend Kadomtsev–Petviashvili (eKP) equation, which appears in the study of multi-component plasmas. By considering Bell’s polynomials, an effective and straightforward way is presented to succinctly derive its bilinear form and soliton solutions. Moreover, the homoclinic breather limit method is employed to construct the breather wave and rogue wave solutions of the equation. Finally, the dynamic behaviors of breather waves, rogue waves and solitary waves are discussed with graphic analysis. It is hoped that our results can be useful for explaining and enriching the dynamic behavior of these KP-type equations.

CFD Simulation of Internal Solitary Wave Using the Volume-of-fluid Method within OpenFOAM

A numerical wave tank based on OpenFOAM was developed to investigate internal solitary waves. The interface of fluids was captured by VOF method. In this paper, comparisons between numerical results and different theoretical solutions were made to evaluate the performance of the numerical wave tank. The result shows that it is a feasible way to further explore the behavior of internal solitary waves by numerical wave tank based on OpenFOAM.

Doubly excited pulse waves on thin liquid films flowing down an inclined plane: An experimental and numerical study.

The interaction patterns between doubly excited pulse waves on thin liquid films flowing down an inclined plane are studied both experimentally and numerically. The effect of varying the film flow rate, interpulse interval, and substrate inclination angle on the pulse interaction patterns is examined. Our results show that different interaction patterns exist for these binary pulses, which include solitary wave behavior, partial or complete pulse coalescence, and pulse noncoalescence. A regime map of these patterns is plotted for each inclination angle examined, parametrized by the film Reynolds number and interpulse interval. Finally, the individual effect of the system parameters mentioned above on the coalescence distance of binary pulses in the "complete pulse coalescence" mode is studied; the results are compared to numerical simulations of the two-dimensional Navier-Stokes equations yielding good agreement.

Impact decimation using alignment of granular spheres

Solitary waves in alignment of elastic beads have been an important area of study. An important and rich area has been the behavior of solitary waves at a boundary, where features such as localization, anomalous behavior in scattering and transmission, quasiequilibrium phase, etc. are being studied. An application area of significance is the design of artificial granular alignments for shock decimation and dispersion. In this review article, we first present a summary and background of these unique features, and some designs in 1D which exploit these features. We further discuss some extensions to higher dimensional systems and their impact decimation ability.

Dynamics of the breathers, rogue waves and solitary waves in the (2+1)-dimensional Ito equation

In this paper, the homoclinic breather limit method is employed to find the breather wave and the rational rogue wave solutions of the (2+1)-dimensional Ito equation. Moreover, based on its bilinear form, the solitary wave solutions of the equation are also presented with a detailed derivation. The dynamic behaviors of breather waves, rogue waves and solitary waves are analyzed with some graphics, respectively. The results imply that the extreme behavior of the breather solitary wave yields the rogue wave for the (2+1)-dimensional Ito equation.

Inhibition of multi-filamentation of high-power laser beams.

We experimentally demonstrate the control and complete elimination of multi-filamentation in condensed matter by varying the focusing geometry. In particular, increasing the input beam power enables the extension of the filament length without generating multi-filaments up to 1400 times the critical power in fused silica at an 800nm wavelength. Furthermore, the generated single filament exhibits spatial solitary wave behavior.