The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP) equation is investigated. The Implicitly Restarted Arnoldi Method for banded matrices with shift-invert was used to solve the linearised spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones-Roberts dispersion curve are shown to be unstable to axisymmetric infinitesimal perturbati...

The equation of motion for a bead in a chain of uncompressed elastic beads in contact that interact via the potential V(delta) approximately delta( n), n>2, delta being overlap, supports solitary waves and does not accommodate sound propagation [V. Nesterenko, J. Appl. Mech. Tech. Phys. 5, 733 (1983)]. We present an iteratively exact solution to describe the solitary wave as a function of mater...

solitary wave solutions to the broer-kaup equations and approximate long water wave equa-tions are considered challenging by using the rst integral method.the exact solutions obtainedduring the present investigation are new. this method can be applied to nonintegrable equa-tions as well as to integrable ones.

Head-on collision and overtaking collision between a KdV solitary wave and an envelope solitary wave are first studied in present paper by using Particle-in-cell (PIC) method in a dusty plasma. There are phase shifts of the KdV solitary wave in both head-on collision and the overtaking collision, while no phase shift is found for the envelop solitary wave in any cases. The remarkable difference...

In this paper, we consider variform exact peakon solutions for four nonlinear wave equations. We show that under different parameter conditions, one nonlinear wave equation can have different exact one-peakon solutions and different nonlinear wave equations can have different explicit exact one-peakon solutions. Namely, there are various explicit exact one-peakon solutions, which are different ...

In this paper, we investigate the (2+1) dimensional long wave-short wave resonance interaction (LSRI) equation and show that it possess the Painlevé property. We then solve the LSRI equation using Painlevé truncation approach through which we are able to construct solution in terms of three arbitrary functions. Utilizing the arbitrary functions present in the solution, we have generated a wide ...

Let d ≥ 4 and let u be a global solution to the focusing masscritical nonlinear Schrödinger equation iut + ∆u = −|u| 4 d u with spherically symmetric H x initial data and mass equal to that of the ground state Q. We prove that if u does not scatter then, up to phase rotation and scaling, u is the solitary wave eQ. Combining this result with that of Merle [15], we obtain that in dimensions d ≥ 4...

The stability of the bright solitary wave solution to the perturbed cubicquintic Schrödinger equation is considered. It is shown that in a certain region of parameter space these solutions are unstable, with the instability being manifested as a small positive eigenvalue. Furthermore, it is shown that in the complimentary region of parameter space there are no small unstable eigenvalues. The pr...

We establish soliton-like asymptotics for finite energy solutions to the Schrödinger equation coupled to a nonrelativistic classical particle. Any solution with initial state close to the solitary manifold, converges to a sum of traveling wave and outgoing free wave. The convergence holds in global energy norm. The proof uses spectral theory and the symplectic projection onto solitary manifold ...

An integrable 2-component Camassa-Holm 2-CH shallow water system is studied by using integral bifurcation method together with a translation-dilation transformation. Many traveling wave solutions of nonsingular type and singular type, such as solitary wave solutions, kink wave solutions, loop soliton solutions, compacton solutions, smooth periodic wave solutions, periodic kink wave solution, si...