Solitary wave dynamics of chains of bistable tensegrity prisms

We perform fluid simulations to examine the effect of ion thermal velocity on the formation and dynamics of solitary waves in an unmagnetized two-component plasma consisting of ions and electrons. Based on the linear and nonlinear fluid theories, some of the previous studies have reported that the plasma with the electron temperature greater than the ion temperature (i.e., Te > Ti) supports ion acoustic solitary waves (IASWs), whereas the plasma with Te ≪ Ti supports electron acoustic waves (EASWs). In this paper, we have considered a wide range of ion temperatures (with fixed electron temperature) to examine the criteria of temperature and thermal velocities in the generation of EASWs and IASWs in plasmas. Our simulation shows that the plasma with Ti > Te possesses two wave modes depending on the ratio of its thermal velocities. When the ratio of electron to ion thermal velocities R = Vthe/Vthi > 1, the system supports the generation of IASWs, whereas for R < 1, it supports the generation of EASWs. The analysis of characteristics like the amplitude, width, and phase speed of these solitary waves implies that the EASWs have a negative potential, whereas the IASWs have the positive potential. The transition from IASWs to EASWs occurs when the phase speed of the solitary wave exceeds the limiting value of 3Vthe. This simulation study presents the detailed investigation of the evolution of EASWs and IASWs generated in plasmas having Ti > Te, which will have implications in modeling such waves in space and laboratory plasmas.

The dynamics of the weak nonlinear matter solitary waves in two-component Bose–Einstein condensates (BEC) with cigar-shaped external potential are investigated analytically by a perturbation method. In the small amplitude limit, the two-components can be decoupled and the dynamics of solitary waves are governed by a variable-coefficient Korteweg–de Vries (KdV) equation. The reduction to the KdV equation may be useful to understand the dynamics of nonlinear matter waves in two-component BEC. The analytical expressions for the evolution of soliton, emitted radiation profiles and soliton oscillation frequency are also obtained.

The dynamics of the weak nonlinear matter solitary waves in a spin-1 condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit, the dynamics of the solitary waves are governed by a variable-coefficient Korteweg-de Vries (KdV) equation. The reduction to the (KdV) equation may be useful to understand the dynamics of nonlinear matter waves in spinor BECs. The analytical expressions for the evolution of soliton show that the small-amplitude vector solitons of the mixed types perform harmonic oscillations in the presence of the trap. Furthermore, the emitted radiation profiles and the soliton oscillation frequency are also obtained.

Influence of static disorder on the dynamics of Fermi resonance solitary waves at the interface between two molecular layers

Optomechanical manipulation of nanoparticles enabling ultimate control over their 3D motion is nowadays one of the most highly demanded links between optics, biology, medicine, microfluidics, etc., paving the way for a plethora of emerging applications from drug delivery to living cells, to new methods of nanofabrication. In this Letter we provide novel type of optical manipulation driven by nonlinear effects and laying on the interface between classical optomechanics and non-linear optics. The formation, stability and the dynamics of optical dissipative solitary waves interacting with dielectric nanoparticles are studied theoretically. A mathematical model describing the optical field and the particles are proposed and the stationary solutions in the form of localized optical waves interacting with nanoparticles are found, their bifurctations are studied. It is shown that the linear stability of the solitary waves is affected by the particles but there are regions in the parameter space where the solitons remain stable. The dynamics of the solitary waves with trapped nanoparticles under the action of the inhomogeneous pump is also studied.

The stability and dynamics of solitary waves propagating along the surface of an inviscid ferrofluid jet in the absence of gravity are investigated analytically and numerically. For the axisymmetric geometry, the problem is shown to be a conservative system with total energy as the Hamiltonian; however, one of the canonical variables differs from those in the classic water-wave problem in the Cartesian coordinate system. The Dirichlet–Neumann operator appearing in the kinetic energy is then expanded as a Taylor series, described in homogeneous powers of the surface displacement. Based on the further analysis of the Dirichlet–Neumann operator, a systematic procedure is proposed to derive reduced model equations of multiple scales in various asymptotic limits from the full Euler equations in the Hamiltonian/Lagrangian framework. Particularly, a fully dispersive model arising from retaining terms valid up to the quartic order in the series expansion of the kinetic energy, which results in quadratic and cubic algebraic nonlinearities in Hamilton's equations and henceforth is abbreviated as the cubic full-dispersion model, is proposed. By comparing bifurcation curves and wave profiles of various types of axisymmetric solitary waves among different model equations, the cubic full-dispersion model is found to agree well with the full Euler equations, even for waves of considerably large amplitudes. The stability properties of axisymmetric solitary waves subjected to longitudinal disturbances are verified with the newly proposed model. Our analytical results, consistent with Saffman's theory, indicate that in the axisymmetric cylindrical system, the stability exchange subjected to superharmonic perturbations also occurs at the stationary point of the speed-energy bifurcation curve. A series of numerical experiments for the stability and dynamics of solitary waves are performed via the numerical time integration of the model equation, and collision interactions between stable solitary waves show non-elastic features.

The dynamics of Fermi resonance solitary waves propagating along two parallel interfaces in a layered organic semiconductor system is investigated both analytically and numerically. It is shown that the interaction between solitary waves leads to their attraction or repulsion, depending on their initial phase difference. In the case of attraction the solitary waves create a bound state, and their centers oscillate in time with respect to their common mass center. The corresponding period of oscillations is calculated. It is found that the amplitudes and widths of the solitary waves also oscillate in time. @S0163-1829~98!01604-X# The search for organic materials for nonlinear optics, photonics, and electronics promoted the development of methods for the preparation of a class of organic structures, namely, organic crystalline superlattices ~OCS!. The latest achievements in this field were demonstrated in a number of publications. 1‐5 At present, investigations in this direction are developing further, therefore the analysis of qualitatively new properties of OCS is very topical and important. The interaction of OCS with light is a fundamental physical problem, as well as of importance for future applications. Papers 6‐10 have been devoted to just such an analysis of these properties of OCS. In particular, different kinds of nonlinear excitations propagating through the superlattice have been discussed ~Fermi resonance interface modes, 7 Fermi resonance interface solitary waves 9,10 !. Here we want to consider the dynamics of two Fermi resonance solitary waves located on two different interfaces of a three-layer system. For convenience, instead of the term ‘‘solitary waves’’ in the following we use the shorter term ‘‘solitons,’’ as frequently done in the literature. These solitons interact with each other due to the penetration of the vibrational field of one of them into the location region of the other one. As we shall see, such ‘‘tunnel’’ coupling results in a considerable change of the dynamics of the solitons as compared to a single soliton. Let us consider a system consisting of three layers of organic semiconductors with two interfaces. We suppose that a film withN11 b-molecular layers lies between two ‘‘halfinfinite’’ crystals made of c molecules. The molecules are labeled as follows: sites ( nx ,n y ,nz<21) are occupied by c molecules, sites ( nx ,n y,0<nz<N) are occupied by b molecules, and sites ( nx ,n y ,N11<nz) are occupied by c molecules again. As in Refs. 7‐10, we assume Fermi resonance between c and b harmonic vibrations, i.e., v c .2v b . For this case the main anharmonic interaction occurs across the interfaces, and has the form

Solitary Wave Formation and Dynamics on Falling Films

We study the dynamics of large amplitude internal solitary waves in shallow water by using a strongly nonlinear long‐wave model. We investigate higher order nonlinear effects on the evolution of solitary waves by comparing our numerical solutions of the model with weakly nonlinear solutions. We carry out the local stability analysis of solitary wave solution of the model and identify an instability mechanism of the Kelvin–Helmholtz type. With parameters in the stable range, we simulate the interaction of two solitary waves: both head‐on and overtaking collisions. We also study the deformation of a solitary wave propagating over non‐uniform topography and describe the process of disintegration in detail. Our numerical solutions unveil new dynamical behaviors of large amplitude internal solitary waves, to which any weakly nonlinear model is inapplicable.

The dynamics of solitary gravity–capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time-dependent solutions, we simplify the full potential flow problem by using surface variables and taking a particular cubic truncation possessing a Hamiltonian with desirable properties. This approximation agrees remarkably well with the full equations for the bifurcation curves, wave profiles and the dynamics of solitary waves for a two-dimensional fluid domain, and with higher-order truncations in three dimensions. Fully localized solitary waves are then computed in the three-dimensional problem and the stability and interaction of both line and localized solitary waves are investigated via numerical time integration of the equations. There are many solitary wave branches, indexed by their finite energy as their amplitude tends to zero. The dynamics of the solitary waves is complex, involving nonlinear focusing of wavepackets, quasi-elastic collisions, and the generation of propagating, spatially localized, time-periodic structures akin to breathers.

The effect of the boundary on the dynamics of solitary waves has been studied. The inverse scattering transformation for the solitary wave equation with boundary condition is treated by the reduction group theory. The effective potential of interaction between the solitary wave and the boundary is found to be same as the Morse potential. The physical mechanism of the soliton oscillation could be interpreted by our results.

We consider the Adlam-Allen (AA) system of partial differential equations, which, arguably, is the first model that was introduced to describe solitary waves in the context of propagation of hydrodynamic disturbances in collisionless plasmas. Here, we identify the solitary waves of the model by implementing a dynamical systems approach. The latter suggests that the model also possesses periodic wave solutions-which reduce to the solitary wave in the limiting case of an infinite period-as well as rational solutions that are obtained herein. In addition, employing a long-wave approximation via a relevant multiscale expansion method, we establish the asymptotic reduction of the AA system to the Korteweg-de Vries equation. Such a reduction is not only another justification for the above solitary wave dynamics, but may also offer additional insights for the emergence of other possible plasma waves. Direct numerical simulations are performed for the study of multiple solitary waves and their pairwise interactions. The stability of solitary waves is discussed in terms of potentially relevant criteria, while the robustness of spatially periodic wave solutions is touched upon via numerical experiments.

Multilump gravity-capillary solitary waves propagating in a fluid of infinite depth are computed numerically. The study is based on a weakly nonlinear and dispersive partial differential equation (PDE) with weak variations in the spanwise direction, a model derived by Akers and Milewski [Stud. Appl. Math., 122 (2009), pp. 249--274]. For a two-dimensional fluid, this model agrees qualitatively well with the full Euler equations for the bifurcation curves, wave profiles, and dynamics of solitary waves. Fully localized solitary waves are then computed for three-dimensional fluids. New symmetric lump solutions are computed by using a continuation method to follow the branch of elevation waves. It is then found that the branch of elevation waves has multiple turning points from which new solutions, consisting of multiple lumps separated by smaller oscillations, bifurcate. Nonsymmetric solitary waves, which also feature a multilump structure, are computed and found to appear via spontaneous symmetry-breaking bifurcations. It is shown that all these new steady solutions are unstable to either longitudinal or transverse perturbations and that the moderate-amplitude depression solitary waves and the linear dispersive waves serve as attractors in the long-time evolution of the instability.

A class of strongly nonlinear metamaterials based on tensegrity concepts is proposed, and the solitary wave dynamics under impact loading is investigated. Such systems can be tuned into elastic hardening or elastic softening regimes by adjusting local and global prestress. In the softening regime these metamaterials are able to transform initially compression pulse into a solitary rarefaction wave followed by oscillatory tail with progressively decreasing amplitude. Interaction of a compression solitary pulse with an interface between elastically hardening and softening materials having correspondingly low-high acoustic impedances demonstrates anomalous behavior: a train of reflected compression solitary waves in the low impedance material; and a transmitted solitary rarefaction wave with oscillatory tail in high impedance material. The interaction of a rarefaction solitary wave with an interface between elastically softening and elastically hardening materials with high-low impedances also demonstrates anomalous behavior: a reflected solitary rarefaction wave with oscillatory tail in the high impedance branch; and a delayed train of transmitted compression solitary pulses in the low impedance branch. These anomalous impact transformation properties may allow for the design of ultimate impact mitigation devices without relying on energy dissipation.

A class of strongly nonlinear metamaterials based on tensegrity concepts is proposed, and the solitary wave dynamics under impact loading is investigated. Such systems can be tuned into elastic hardening or elastic softening regimes by adjusting local and global prestress. In the softening regime these metamaterials are able to transform initially compression pulse into a solitary rarefaction wave followed by oscillatory tail with progressively decreasing amplitude. Interaction of a compression solitary pulse with an interface between elastically hardening and softening materials having correspondingly low-high acoustic impedances demonstrates anomalous behavior: a train of reflected compression solitary waves in the low impedance material; and a transmitted solitary rarefaction wave with oscillatory tail in high impedance material. The interaction of a rarefaction solitary wave with an interface between elastically softening and elastically hardening materials with high-low impedances also demonstrates anomalous behavior: a reflected solitary rarefaction wave with oscillatory tail in the high impedance branch; and a delayed train of transmitted compression solitary pulses in the low impedance branch. These anomalous impact transformation properties may allow for the design of ultimate impact mitigation devices without relying on energy dissipation.