solitons are ubiquitous and exist in almost every area from sky to bottom. for solitons to appear, the relevant equation of motion must be nonlinear. in the present study, we deal with the korteweg-devries (kdv), modied korteweg-de vries (mkdv) and regularised longwave (rlw) equations using homotopy perturbation method (hpm). the algorithm makes use of the hpm to determine the initial expansio...

The characteristics of arbitrary amplitude dust ion acoustic solitary waves (DIASWs) are studied in unmagnetized dusty plasmas whose constituents are cold uid ions, nonextensive electrons and stationary negative/positive dust particles. The pseudopotential approach has been used to investigate the structure of localized waves. It is found that, solitary waves exist in a definite interval for th...

In a two-uid system where the lower uid is bounded below by a rigid bottom and the upper uid is bounded above by a free surface, two kinds of solitary waves can propagate along the interface and the free surface: classical solitary waves characterized by a solitary pulse or generalized solitary waves with nondecaying oscillations in their tails in addition to the solitary pulse. The classical s...

A model equation for gravity-capillary waves in deep water is proposed. This model is a quadratic approximation of the deep water potential flow equations and has wavepacket-type solitary wave solutions. The model equation supports line solitary waves which are spatially localized in the direction of propagation and constant in the transverse direction, and lump solitary waves which are spatial...

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...

The possible solitary wave solutions for a general Boussinesq (GBQ) type fluid model are studied analytically. After proving the non-Painlevé integrability of the model, the first type of exact explicit travelling solitary wave with a special velocity selection is found by the truncated Painlevé expansion. The general solitary waves with different travelling velocities can be studied by casting...

In this paper, the solitary waves in coupled nonlinear Schrodinger equations are classified into infinite families. For each of the first three families, the parameter region is specified and the parameter dependence of its solitary waves described and explained. We found that the parameter regions of these solution families are novel and irregular, and the parameter dependence of the solitary ...

Internal solitary waves are hump-shaped, large-amplitude waves that are physically analogous to surface waves except that they propagate within the fluid, along density steps that typically characterize the layered vertical structure of lakes, oceans and the atmosphere. As do surface waves, internal solitary waves may overturn and break, and the process is thought to provide a globally signific...

We study here the existence of solitary wave solutions of a generalized twocomponent Camassa-Holm system. In addition to those smooth solitary-wave solutions, we show that there are solitary waves with singularities: peaked and cusped solitary waves. We also demonstrate that all smooth solitary waves are orbitally stable in the energy space. We finally give a sufficient condition for global str...

We examine the dynamics of two bright solitary waves with a negative nonlinear term. The observed repulsion between two solitary waves – when these are in an antisymmetric combination – is attributed to conservation laws. Slight breaking of parity, in combination with weak relaxation of energy, leads the two solitary waves to merge. The effective repulsion between solitary waves requires certai...