Nonreciprocal Head-on Collision Between Two Nonlinear Solitary Waves in Granular Metamaterials with an Interface

In this work,the head-on collision and transmission with nonreciprocal properties of opposite propagating solitary waves are studied,in which the interface between different granular chains is considered.Due to the discontinuity of two periodic granular systems,the transmitted and reflected solitary waves are produced.The head-on collision appears at the interface and the reductive perturbation method is applied to derive the generated solitary waves.According to the derivation and numerical simulation,we can find that the transmitted and reflected solitary waves can propagate with the same speed when they locate at the same chain.Moreover,the influences of both the arrangement and prestress are discussed.It is found that the amplitude and velocity of solitary waves become larger because of a bigger prestress,which result in the nonreciprocal collision and transmission in the granular mechanical metamaterials.This study is expected to be helpful for the design and application of elastic wave metamaterials and mechanical diodes with nonlinear solitary waves.

On a Class of Solitary Wave Solutions of Atmospheric Nonlinear Equations

In this paper, an attempt is made to study some interesting results of the coupled nonlinear equations in the atmosphere. By introducing a phase angle function ζ, it is shown that the atmospheric equations in the presence of specific forcing exhibit the exact and explicit solitary wave solutions under certain conditions.

Formation of Nonlinear Solitary Vortical Structures by Coupled Electrostatic Drift and Ion-Acoustic Waves

Propagation of coupled electrostatic drift and ion-acoustic waves（DIAWs） is presented. It is shown that nonlinear solitary vortical structures can be formed by low-frequency coupled electrostatic DIAWs. Primary waves of distinct（small, intermediate and large） scales are considered. Appropriate set of 3 D equations consisting of the generalized Hasegawa-Mima equation for the electrostatic potential（involving both vector and scalar nonlinearities） and the equation of motion of ions parallel to magnetic field are obtained. According to experiments of laboratory plasma mainly focused to large scale DIAWs, the possibility of self-organization of DIAWs into the nonlinear solitary vortical structures is shown analytically. Peculiarities of scalar nonlinearities in the formation of solitary vortical structures are widely discussed.

Weak Nonlinear Matter Waves in a Trapped Spin-1 Condensates

The dynamics of the weak non//near matter sofitary 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-coetficient 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.

NONLINEAR CNOIDAL WAVES AND SOLITARY WAVES IN ATMOSPHERE

In this paper, starting with the equations describing the atmospheric motion and by arelatively simple method, we find that, nearby the mechanical equilibrium point, all thefinite amplitude nonlinear inertia waves, internal gravity waves and Rossby waves in thedispersive atmosphere satisfy the KdV (Korteweg-de Vries) equation, its solution being thecnoidal waves and solitary waves. For the finite amplitude Rossby waves, we find the newdispersive relation which is different from the Rossby formula and contains the amplitudeparameter. It is shown that the larger the amplitude and width, the faster are the wavesfor the finite amplitude inertia waves and internal gravity waves, and the slower are thewaves for the Rossby solitary waves, to which perhaps the polar vortex and the blocking orcut-off systems belong. This treatise gives the nonlinear waves a new way and inspires usto study the nonlinear adjustment process and evolution process and the turbulence structure.

LOCAL ATTRACTORS FOR WEAKLY DAMPED FORCED KdV EQUATION IN THIN 2D DOMAINS

The existence of local attractors in thin 2D domains far the weakly damped forced KdV equation, whose principal operator is a non-self adjoint and non-sectorial one is given.

BIFURCATIONS AND NEW EXACT TRAVELLING WAVE SOLUTIONS OF THE COUPLED NONLINEAR SCHRDINGER-KdV EQUATIONS

By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrdinger-KdV equations are studied. Based on this method, all phase portraits of the system in the parametric space are given. All possible bounded travelling wave solutions such as solitary wave solutions and periodic travelling wave solutions are obtained. With the aid of Maple software, the numerical simulations are conducted for solitary wave solutions and periodic travelling wave solutions to the coupled nonlinear Schrdinger-KdV equations. The results show that the presented findings improve the related previous conclusions.