Related papers: Solitary Waves in Massive Nonlinear S^N-Sigma Mode…
We describe the kink solitary waves of a massive non-linear sigma model with an ${\mathbb S}^2$ sphere as the target manifold. Our solutions form a moduli space of non-relativistic solitary waves in the long wavelength limit of…
Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schr\"odinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, that span a…
The paper is devoted to analysis of different models that describe waves in fluid-filled and gas-filled elastic tubes and development of methods of calculation and numerical analysis of solutions with solitary waves and kinks for these…
Roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localized packet and which preserves this localization in time. A solitary wave which has a non-vanishing angular momentum is called vortex. We…
The interaction of a solitary wave and a slowly varying mean background or flow for the Serre-Green-Naghdi (SGN) equations is studied using Whitham modulation theory. The exact form of the three SGN-Whitham modulation equations -- two for…
In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two,…
It is known that there are nonlinear wave equations with localized solitary wave solutions. Some of these solitary waves are stable (with respect to a small perturbation of initial data) and have nonzero spin (nonzero intrinsic angular…
In this paper the whole kink varieties arising in several massive non-linear Sigma models whose target space is the torus ${\mathbb S}^1\times{\mathbb S}^1$ are analytically calculated. This possibility underlies the construction of…
We review recent results on global attractors of U(1)-invariant dispersive Hamiltonian systems. We study several models based on the Klein-Gordon equation and sketch the proof that in these models, under certain generic assumptions, the…
The stability of topological solitary waves and pulses in one-dimensional nonlinear Klein-Gordon systems is revisited. The linearized equation describing small deviations around the static solution leads to a Sturm-Liouville problem, which…
It is shown that the topological discrete sine-Gordon system introduced by Speight and Ward models the dynamics of an infinite uniform chain of electric dipoles constrained to rotate in a plane containing the chain. Such a chain admits a…
We consider a scalar Hamiltonian nonlinear wave equation formulated on networks; this is a non standard problem because these domains are not locally homeomorphic to any subset of the Euclidean space. More precisely, we assume each edge to…
Starting from the von Neumann-Maxwell equations for the Wigner quasi-probability distribution and for the self-consistent electric field, the quantum analog of the classical single-wave model has been derived. The linear stability of the…
We obtain the most general matrix criterion for stability and instability of multi-component solitary waves considering a system of $N$ incoherently coupled nonlinear Schrodinger equations. Soliton stability is studied as a constrained…
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain…
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient…
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…
We consider a system of coupled nonlinear Schr{\"o}dinger equations in one space dimension. First, we prove the existence of multi-speed solitary waves, i.e solutions to the system with each component behaving at large times as a solitary…
A family of solitary waves is constructed in Frenkel-Kontorova model and its continuum and quasi-continuum approximations. Each solitary waves is characterised by the number of local maxima in its profile and a relation between external…
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…