Related papers: Solitary waves for dispersive equations with Coifm…
We improve the decay argument by [Bona and Li, J. Math. Pures Appl., 1997] for solitary waves of general dispersive equations and illustrate it in the proof for the exponential decay of solitary waves to steady Degasperis-Procesi equation…
Generalized solitary waves with exponentially small non-decaying far field oscillations have been studied in a range of singularly-perturbed differential equations, including higher-order Korteweg-de Vries (KdV) equations. Many of these…
We consider the spectral stability of solitary wave solutions \phi(x)e^{-i\omega t} to the nonlinear Dirac equation in any dimension. This equation is well-known to theoretical physicists as the Soler model (or, in one dimension, the…
An explanation is given for previous numerical results which suggest a certain bifurcation of `vector solitons' from scalar (single-component) solitary waves in coupled nonlinear Schroedinger (NLS) systems. The bifurcation in question is…
We prove that the 2D finite depth capillary water wave equations admit no solitary wave solutions. This closes the existence/non-existence problem for solitary water waves in 2D, under the classical assumptions of incompressibility and…
We study the Korteweg-de Vries-type equation dt u=-dx(dx^2 u+f(u)-B(t,x)u), where B is a small and bounded, slowly varying function and f is a nonlinearity. Many variable coefficient KdV-type equations can be rescaled into this equation. We…
In this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we…
We consider the focusing nonlinear Schr\"odinger equation on a large class of rotationally symmetric, noncompact manifolds. We prove the existence of a solitary wave by perturbing off the flat Euclidean case. Furthermore, we study the…
We consider the electromagnetic waves propagating in the system of coupled waveguides. One of the system components is a standard waveguide fabricated from nonlinear medium having positive refraction and another component is a waveguide…
The KP-I equation arises as a weakly nonlinear model equation for gravity-capillary waves with Bond number $\beta>1/3$, also called strong surface tension. This equation has recently been shown to have a family of nondegenerate, symmetric…
We study spherically symmetric solutions of semilinear wave equations in the case where the nonlinearity satisfies the null condition on extremal Reissner--Nordstrom black hole spacetimes. We show that solutions which arise from…
We establish spectral, linear, and nonlinear stability of the vanishing and slow-moving travelling waves that arise as time asymptotic solutions to the Fisher-Stefan equation. Nonlinear stability is in terms of the limiting equations that…
We demonstrate the existence of a new class of two-component vector solitary waves in which dispersion coefficients have of opposite signs. Stability is achieved by inclusion of an additional linear coupling between the vector components…
We study the existence of solitary-wave solutions and some of their properties for a general multicomponent long-wave-short-wave interaction system. The system considered here describes the nonlinear interaction of multiple short waves with…
In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal…
We construct bi-frequency solitary waves of the nonlinear Dirac equation with the scalar self-interaction (the Soler model) and the Dirac--Klein--Gordon with Yukawa self-interaction. These solitary waves provide a natural implementation of…
This paper is concerned with the periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficient. Such a model arises from the forced vibrations of a nonhomogeneous string and propagation of…
In this paper, we study the existence of positive solutions to the nonlinear elliptic system, which is derived from taking the nonrelativistic limit of the nonlinear Maxwell-Klein-Gordon equations under the decomposition of waves functions…
The Whitham equation is a nonlocal shallow water-wave model which combines the quadratic nonlinearity of the KdV equation with the linear dispersion of the full water wave problem. Whitham conjectured the existence of a highest, cusped,…
A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary…