Solitary surface acoustic waves and bulk solitons in nanosecond and picosecond laser ultrasonics

Recent achievements of nonlinear acoustics concerning the realization of solitons and solitary waves in crystals and their surfaces attained by nanosecond and picosecond laser ultrasonics are discussed and compared. The corresponding pump-probe setups are described, which allow an all-optical contact-free excitation and detection of short strain pulses in the broad frequency range between 10 MHz and about 300 GHz. The formation of solitons in the propagating longitudinal strain pulses is investigated for nonlinear media with intrinsic lattice-based dispersion. The excitation of solitary surface acoustic waves is realized by a geometric film-based dispersion effect. Future developments and potential applications of nonlinear nanosecond and picosecond ultrasonics are discussed.     

Nonlinear Longitudinal Strain Waves in a Solid Exposed to Pulsed Laser Radiation

The propagation of longitudinal strain waves in a solid with quadratic nonlinearity of elastic continuum was studied in the context of a model that takes into account the joint dynamics of elastic displacements in the medium and the concentration of the laser-induced point defects. The input equations of the problem are reformulated in terms of only the total displacements of the medium points. In this case, the presence of structural defects manifests itself in the emergence of a delayed response of the system to the propagation of the strain-related perturbations, which is characteristic of media with relaxation or memory. The model equations describing the nonlinear displacement wave were derived with allowance made for the values of the relaxation parameter. The influence of the generation, relaxation, and the strain-induced drift of defects and the flexoelectricity on the propagation of this wave was analyzed. It is shown that, for short relaxation times of defects, the strain can propagate in the form of both shock fronts and solitary waves (solitons). Exact solutions depending on the type of relation between the coefficients in the equation and describing both the shock-wave structures and the evolution of solitary waves are presented. In the case of longer relaxation times, shock waves do not form and the strain wave propagates only in the form of solitary waves or a train of solitons. The contributions of the finiteness of the defect-recombination rate and the flexoelectricity to linear elastic moduli and spatial dispersion are determined.     

南海北部海域内波环境下声传播损失起伏统计特性

浅海内波会引起声传播能量随时间的起伏变化,进而影响水声设备的工作性能.本文利用2015年南海北部一次浅海声场起伏实验数据,对比分析了浅海线性内波和孤立子内波条件下的声传播损失统计特性.在孤立子内波条件下,声传播损失起伏明显加剧,可达11 dB,且分布明显展宽,相对于线性内波的环境,声传播损失起伏可增加5 dB.从简正波...     

Observation of spin-wave envelope Dark solitons in ferromagnetic films

Microwave spin-wave envelope dark solitons were experimentally observed for the first time. Dark solitons with zero minimum amplitude were generated by two-frequency excitation of input spin waves with a fixed amplitude. Nonlinear interaction between these two traveling waves gave rise to periodic sequences of dark solitons in a ferromagnetic film.     

Do solitonlike self-similar waves exist in nonlinear optical media?

We show analytically that bright and dark spatial self-similar waves can propagate in graded-index amplifiers exhibiting self-focusing or self-defocusing Kerr nonlinearities. The intensity profiles of the novel waves are identical with those of fundamental bright or dark spatial solitons supported by homogeneous passive waveguides with the same type of nonlinearity. Thus, we reveal a previously unnoticed connection between spatial solitons and self-similar waves. We also suggest that the discovered self-similar waves can be used in a promising scheme for the amplification and focusing of spatial solitons in future all-optical networks.     

Solitons in nonintegrable systems

We introduce the concept of this special focus issue on solitons in nonintegrable systems. A brief overview of some recent developments is provided, and the various contributions are described. The topics covered in this focus issue are the modulation of solitons, bores, and shocks, the dynamical evolution of solitary waves, and existence and stability of solitary waves and embedded solitons.     

Electromagnetic envelope solitons in magnetized plasma

A multiple scales technique is employed to solve the fluid-Maxwell equations describing a weakly nonlinear circularly polarized electromagnetic pulse in magnetized plasma. A nonlinear Schrödinger-type (NLS) equation is shown to govern the amplitude of the vector potential. The conditions for modulational instability and for the existence of various types of localized envelope modes are investigated in terms of relevant parameters. Right-hand circularly polarized (RCP) waves are shown to be modulationally unstable regardless of the value of the ambient magnetic field and propagate as bright-type solitons. The same is true for left-hand circularly polarized (LCP) waves in a weakly to moderately magnetized plasma. In other parameter regions, LCP waves are stable in strongly magnetized plasmas and may propagate as dark-type solitons (electric field holes). The evolution of envelope solitons is analyzed numerically, and it is shown that solitons propagate in magnetized plasma without any essential change in amplitude and shape.     

等离子体中Langmuir波、横波和离子声波相互作用过程的孤立子行为

我们用Zakharov方程描述等离子体中Langmuir波、横波和离子声波的非线性相互作用,通过研究系统稳态的Sagdeev势的性质,讨论了该系统中孤立子可能存在的条件;同时和体系的极小能量状态相联系,构造了体系的Liapunov泛函,研究了孤立子的Liapunov稳定性。我们所采用的方法是完全非线性的,得到的稳定性判据在横波和Langmuir波解耦情况下退化为文献[8]的结果。 关键词：     

Envelope self-similar solutions for the nonautonomous and inhomogeneous nonlinear Schrödinger equation

By means of the similarity transformation connecting with the solvable stationary equation, the self-similar combined Jacobian elliptic function solutions and fractional form solutions of the generalized nonlinear Schrödinger equation (NLSE) are obtained when the dispersion, nonlinearity, and gain or absorption are varied. The propagation dynamics in a periodic distributed amplification system is investigated. Self-similar cnoidal waves and corresponding localized waves including bright and dark similaritons (or solitons) for NLSE and arch and kink similaritons (or solitons) for cubic-quintic NLSE are analyzed. The results show that the intensity and the width of chirped cnoidal waves (or similaritons) change more distinctly than that of chirp-free counterparts (or solitons).     

Two-dimensional bright solitons in dipolar Bose-Einstein condensates

We analyze the physics of bright solitons in 2D dipolar Bose-Einstein condensates. These solitons, which are not possible in short-range interacting gases, constitute the first realistic proposal of fully mobile stable 2D solitons in ultracold gases. In particular, we discuss the necessary conditions for the existence of stable 2D bright solitary waves by means of a 3D analysis of the lowest-lying excitations. We show that the anisotropy of the dipolar potential is crucial, since sufficiently large dipolar interactions can destabilize the 2D soliton. Additionally, we study the scattering of solitary waves, which, contrary to the contact-interacting case, is inelastic and could lead to fusion of the waves. Finally, the experimental possibilities for observability are discussed.     

Dielectric constant of graphene-on-polarized substrate: A tight-binding model study

By using the bifurcation theory of planar dynamical systems and the qualitative theory of differential equations, we studied the dynamical behaviours and exact travelling wave solutions of the modified generalized Vakhnenko equation (mGVE). As a result, we obtained all possible bifurcation parametric sets and many explicit formulas of smooth and non-smooth travelling waves such as cusped solitons, loop solitons, periodic cusp waves, pseudopeakon solitons, smooth periodic waves and smooth solitons. Moreover, we provided some numerical simulations of these solutions.     

Coupled modulational instability of copropagating spin waves in magnetic thin films

This letter reports the first results on the coupled modulational instability of copropagating spin waves in a magnetic film. Strong instability was observed for the two waves with either attractive or repulsive nonlinearity. If the two waves have attractive nonlinearity, the instability leads to the formation of bright solitons. If the two waves have repulsive nonlinearity, the process results in the formation of black solitons. The instability was also observed for the two waves in separated attractive-repulsive nonlinearity regimes.     

Supernonlinear ion-acoustic waves in a dusty plasma

An exact solution is obtained for the equations that describe nonlinear ion-acoustic waves in a dusty plasma. It is shown that the solution can be in the form of nonlinear periodic waves, solitons, and supernonlinear waves whose trajectories envelope one or several separatrices in the phase portrait of the wave. Profiles of physical quantities in the wave are constructed. The supernonlinear waves are shown to be of two types, subsonic (type 1) and supersonic (type 2). Existence regions of supernonlinear waves of both types and solitons are constructed in the plane of the problem parameters.     

Abundant different types of exact soliton solution to the (4+1)-dimensional Fokas and (2+1)-dimensional breaking soliton equations

The prime objective of this paper is to explore the new exact soliton solutions to the higher-dimensional nonlinear Fokas equation and(2+1)-dimensional breaking soliton equations via a generalized exponential rational function(GERF) method. Many different kinds of exact soliton solution are obtained, all of which are completely novel and have never been reported in the literature before. The dynamical behaviors of some obtained exact soliton solutions are also demonstrated by a choice of appropriate values of the free constants that aid in understanding the nonlinear complex phenomena of such equations. These exact soliton solutions are observed in the shapes of different dynamical structures of localized solitary wave solutions, singular-form solitons, single solitons,double solitons, triple solitons, bell-shaped solitons, combo singular solitons, breather-type solitons,elastic interactions between triple solitons and kink waves, and elastic interactions between diverse solitons and kink waves. Because of the reduction in symbolic computation work and the additional constructed closed-form solutions, it is observed that the suggested technique is effective, robust, and straightforward. Moreover, several other types of higher-dimensional nonlinear evolution equation can be solved using the powerful GERF technique.     

The Fermi-Pasta-Ulam recurrence and related phenomena for 1<Emphasis Type="Italic">D</Emphasis> shallow-water waves in a finite basin

Different regimes of the Fermi-Pasta-Ulam (FPU) recurrence are simulated numerically for fully nonlinear “one-dimensional” potential water waves in a finite-depth flume between two vertical walls. In such systems, the FPU recurrence is closely related to the dynamics of coherent structures approximately corresponding to solitons of the integrable Boussinesq system. A simplest periodic solution of the Boussinesq model, describing a single soliton between the walls, is presented in analytic form in terms of the elliptic Jacobi functions. In the numerical experiments, it is observed that depending on the number of solitons in the flume and their parameters, the FPU recurrence can occur in a simple or complicated manner, or be practically absent. For comparison, the nonlinear dynamics of potential water waves over nonuniform beds is simulated, with initial states taken in the form of several pairs of colliding solitons. With a mild-slope bed profile, a typical phenomenon in the course of evolution is the appearance of relatively high (rogue) waves, while for random, relatively short-correlated bed profiles it is either the appearance of tall waves or the formation of sharp crests at moderate-height waves.     

Dynamics of solitons in a nonintegrable version of the modified Korteweg-de Vries equation

Nonlinear wave dynamics is discussed using the extended modified Korteweg-de Vries equation that includes the combination of the third- and fifth-order terms and is valid for waves in a three-layer fluid with so-called symmetric stratification. The derived equation has solutions in the form of solitary waves of various polarities. At small amplitudes, they are close to solitons of the modified Korteweg-de Vries equation. However, the height of large-amplitude solutions has a limit approaching which solitary waves widen and acquire a table like shape similar to soluitons of the Gardner equation. Numerical calculations confirm that the collision of solitons of the derived equation is inelastic. Inelasticity is the most pronounced in the interaction of unipolar pulses. The direction of the shift of the phase of the higher-amplitude soliton owing to the interaction of solitons of different polarities depends on the amplitudes of the pulses.     

Multiple-mode wave solutions in Vakhnenko equation

A new type of wave solutions, called as multiple-mode waves, which can be expressed in the superposition forms of more than two types of single-mode waves of Vakhnenko equation have been investigated in this Letter. A new general method for obtaining the multiple-mode waves is proposed, based on which four cases of the possible forms of wave solutions with two-mode have been derived. The explicit expressions of the two-mode waves as well as the existence conditions have been presented, which may be the nonlinear combinations between periodic waves, solitons, compactons, etc., with different wave speeds, respectively. It is pointed out that more complicated multiple-mode waves with more than three single-mode waves can be derived accordingly, which can be used to reveal the evolution of interactions between different types of waves, especially between various solitons.     

Soliton dynamics in the complex modified KdV equation with a periodic potential

We study the existence and stability of stationary and moving solitary waves in a periodically modulated system governed by an extended cmKdV (complex modified Korteweg-de Vries) equation. The proposed equation describes, in particular, the co-propagation of two electromagnetic waves with different amplitudes and orthogonal linear polarizations in a liquid crystal waveguide, the stronger (nonlinear) wave actually carrying the soliton, while the other (a nearly linear one) creates an effective periodic potential. A variational analysis predicts solitons pinned at minima and maxima of the periodic potential, and the Vakhitov-Kolokolov criterion predicts that some of them may be stable. Numerical simulations confirm the existence of stable stationary solitary waves trapped at the minima of the potential, and show that persistently moving solitons exist too. The dynamics of pairs of interacting solitons is also studied. In the absence of the potential, the interaction is drastically different from the behavior known in the NLS (nonlinear Schrödinger) equation, as the force of the interaction between the cmKdV solitons is proportional to the sine, rather than cosine, of the phase difference between the solitons. In the presence of the potential, two solitons placed in one potential well form a persistently oscillating bound state.     

Multiwave interaction solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation

To construct a class of new multiwave interaction solutions for the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation, we calculate different types of interaction solutions among solitons, periodic waves and rational waves using the direct algebraic method together with the inheritance solving skill. Moreover, a new algorithm is proposed with the aid of the simplified Hirota method, the conjugated parameters assignment and long wave limit strategies, from which multiwave interaction solutions among solitons, breathers and lump waves are generated.     

尘埃等离子体中非线性波的叠加效应及稳定性问题

研究了小的有限振幅的无磁场尘埃等离子体中的非线性波.在一维情况下由Kortewegde Veries(KdV)方程来描述,考虑了二维情况下尘埃等离子体中尘埃颗粒上电荷的变化效应以及双温度离子效应后,尘埃等离子体受到横向高阶扰动后动力学方程由Kadomtsev-Petviashvili(KP)方程来描述.在此基础上,研究了以任意夹角传播的两个及三个孤立子的相互作用问题,考虑非线性效应后振幅相等的双孤立子在相互作用区域内振幅最大值是单个孤立子振幅的4倍,振幅相等的三孤立子在相互作用区域内振幅最大值是单个孤立子振幅的9倍.研究还表明波的传播方向受到横向高阶扰动后是稳定的.