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...

The existence of solitary-wave solutions to the three-dimensional water-wave problem with strong surface-tension effects is predicted by the KP-I model equation. The term solitary wave describes any solution which has a pulse-like profile in its direction of propagation, and the KP-I equation admits explicit solutions for three different types of solitary wave. A line solitary wave is spatially...

where 3 depends’on the cross section area of the topography [see Miles’ Eqs. (5.2) and (5.3)‘]. A year later, VandenBroeck published his discovery of two smooth solitary wave solutions for the same physical model but from the perspective of direct numerical integration of Laplace equation with a free boundary and with nonlinear boundary conditions.2 One of his solitary waves is higher than the ...

Solitary wave solutions to the Broer-Kaup equations and approximate long water wave equations are considered challenging by using the rst integral method.The exact solutions obtained during the present investigation are new. This method can be applied to nonintegrable equations as well as to integrable ones.

In this paper, we study a class of nonlinear Schrödinger equations (NLS) which admit families of small solitary wave solutions. We consider solutions which are small in the energy space H, and decompose them into solitary wave and dispersive wave components. The goal is to establish the asymptotic stability of the solitary wave and the asymptotic completeness of the dispersive wave. That is, we...

Soliton perturbation theory is used to determine the evolution of a solitary wave described by a perturbed nonlinear Schrödinger equation. Perturbation terms, which model wide classes of physically relevant perturbations, are considered. An analytical solution is found for the first-order correction of the evolving solitary wave. This solution for the solitary wave tail is in integral form and ...

The ambipolar radial electric field in a nonaxisymmetric plasma can be described by a nonlinear diffusion equation. This equation is shown to possess solitary wave solutions. A model nonlinear diffusion equation with a cubic nonlinearity is studied. An explicit analytic step-like form for the solitary wave is found. It is shown that the solitary wave solutions are linearly stable against all bu...

Solitary-wave solutions of a nonlinearly dispersive equation are considered. It is found that solitary waves are peaked or smooth waves, depending on the wave speed. The stability of the smooth solitary waves also depends on the wave speed. Orbital stability is proved for some wave speeds, while instability is proved for others.

The objective of this paper is to study the existence of solitary wave solutions of a fifth order model equation for steady capillary-gravity waves over a bump with the Bond number near 1/3. We proved that there exist solitary wave solutions of the model equation for a sufficiently smooth compact bump. Key-Words: Steady capillary-gravity wave, Solitary wave solution, Compact bump.