We study the shape of solitary wave pulses that propagate in an infinite chain of beads initially in contact with no compression. For this system, the repulsive force between two adjacent beads is proportional to the pth power of the distance of approach of their centers with p = 3 2 . It is known that solitary wave solutions exist for such a system when p > 1. We prove extremely fast, double-e...

We prove that the Cauchy problem for a certain sixth order hyperelastic dispersive equation is globally well-posed in a natural space. We also show that there exist solitary wave solutions u(x, y, t) = φc(x − ct, y) that come from an associated variational problem. Such solitary waves are nonlinearly stable in the sense that if a solution is initially close to the set of such solitary waves, it...

We study the conditions for soliton-like wave propagation in the Photorefractive (PR) and electro-optic (i.e., Pockels) material, by using Nonlinear Schrodinger (NLS) equation. The complete NLS equation is solved analytically and numerically by transforming it into the phase space. Our results clearly show the existence of both the dark and bright solitary solutions for the PR medium. Interesti...

Self-focusing of an intense optical beam in a plasma is studied, including the nonlinear effects of both the relativistic electron mass and the ponderomotive potential due to the electromagnetic wave. An exact steady-state asymptotic solution of beam propagation in a localized solitary waveform is obtained in slab geometry. Amplitude-width scaling relations are obtained, which imply that the wi...

The behavior of linear and nonlinear dust acoustic waves (DAWs) in an unmagnetized plasma including inertialess electrons and positrons, ions, and mobile positive/negative dust grains are studied. Reductive perturbation method is employed for small and finite amplitude DAWs. To investigate the solitary waves, the Korteweg–de Vries (KdV) equation is derived and the solution is presented. B...

The general solution is found to a bilinear reduction of the higher order nonlinear Schrödinger equation. Except for the previously known special cases having multisoliton solutions, the solution has the form of a single envelope solitary wave or wave train for all other values of the parameters. We conjecture that the generic solution is limited to such a narrow class of functions because the ...

dust acoustic (da) solitary waves are investigated in an unmagnetized dusty plasma comprising of fluid warm dust particles and kappa distributed ions. we assume the electron number density to be sufficiently depleted in this fluid model, i.e., ne  nd . we consider the usual ad hoc damping term, involving the damping rate  due to the dust–neutral collisions; and derived the modified dis...

Double cnoidal waves of the Korteweg-de Vries equation are studied by direct solution of the nonlinear boundary value problem. These double cnoidal waves, which are the spatially periodic generalization of the well-known double soliton, are exact solutions with two independent phase speeds. The equation is written in terms of two phase variables and expanded in two-dimensional Fourier series. T...

Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. Attention is restricted to solutions that, for the appropriate choice of certain constant parameters, reduce to solutions of the reduced Ostrovsky equation. It is shown how the nature of the waves may be categorized in a simple way by considering the value of a certain single combination ...