We provide the first construction of exact solitary waves of large amplitude with an arbitrary distribution of vorticity. We use continuation to construct a global connected set of symmetric solitary waves of elevation, whose profiles decrease monotonically on either side of a central crest. This generalizes the classical result of Amick and Toland.

In this paper we study the solitary waves for the coupled Schrödinger Maxwell equations in three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed L norm. We study the asymptotic behavior and the smoothness of these solutions. We show also the fact that the eigenvalues are negative and the first one is isolated.

Considered herein is the stability problem of solitary wave solutions of a generalized Ostrovsky equation, which is a modification of the Korteweg-de Vries equation widely used to describe the effect of rotation on surface and internal solitary waves or capillary waves.

A highly efficient and accurate numerical scheme for initial and boundary value problems of a two-dimensional Boussinesq system which describes three-dimensional water waves is used to study in details the oblique interaction of a solitary wave and the evolution of solitary waves coming out of a narrower channel.

Symmetry and monotonicity properties of solitary water-waves of positive elevation with supercritical values of parameter are established for an arbitrary vorticity. The proof uses the detailed knowledge of asymptotic decay of supercritical solitary waves at infinity and the method of moving planes.

Solitary acoustic pulses can propagate along the surface of a coated homogeneous and inhomogeneous medium. It is shown how these nonlinear surface acoustic waves evolve out of initial pulselike conditions generated by pulsed laser excitation and how they can be monitored by optical detection. The solitary pulse shapes at the surface are computed on the basis of an evolution equation with nonloc...

The basic theory of internal solitary waves is reviewed, with the main emphasis on applications to the many observations of such waves in shallow coastal seas, fjords, lakes and in the atmospheric boundary layer. Commencing with the equations of motion for an inviscid, incompressible density-stratified fluid, we describe asymptotic reductions to model long-wave equations, including the well-kno...

[1] Electrostatic solitary structures have been observed in the Earth’s magnetosheath by the Cluster spacecraft. Recent theoretical work has suggested that these solitary structures are modeled by electron acoustic solitary waves existing in a four-component plasma system consisting of core electrons, two counter-streaming electron beams, and one species of background ions. In this paper, the e...

In this paper, a generalized Camassa–Holm equation is studied by using the integral bifurcation method. Many travelling waves such as peaked compacton, compacton, peaked solitary wave, solitary wave and kink-like wave are found. In some parameter conditions, exact parametric representations of these travelling waves in explicit form and implicit form are obtained. 2008 Elsevier Inc. All rights ...