Related papers: Solitary waves in the Nonlinear Dirac Equation
We examine solitary waves in classical Heisenberg chains with an uniaxial anisotropy and a parallel magnetic field in a continuum approach. The boundary conditions commonly used are generalized to nonlinear spin wave states, which…
We study the nonlinear Schr\"odinger equation with a competing cubic-quintic power law nonlinearity on the waveguide domain $\mathbb R_x \times \mathbb T_{L_y}$. This model is globally well-posed and admits line solitary wave solutions,…
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrowband in frequency but not necessarily with narrow angular distributions the developed asymptotic…
Using a modified version of Weinstein's argument for constrained minimization in nonlinear dispersive equations, we prove existence of solitary waves in fully nonlocally nonlinear equations, as long as the linear multiplier is of positive…
In this paper we study the solitary waves for the coupled Schr\"odinger - Maxwell equations in three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed $L^2$ norm. We study the…
Solitary wave and soliton solutions of nonlinear equations are well known for physicists. A soliton is a solitary wave with some outstanding features which make it reasonable to be studied seriously in nonlinear systems. In fact most of the…
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 the NLS system of the third-harmonic generation, which was introduced by Sammut. Our interest is in solitary wave solutions and their stability properties. The recent work of Oliveira and Pastor, discussed global well-posedness…
In this paper we consider a three-component system of one dimensional long wave-short wave interaction equations. The system has two-parameter family of solitary wave solutions. We prove orbital stability of the solitary wave solutions…
In this paper we study a family of one-dimensional stationary cubic nonlinear Schr\"odinger (NLS) equations with periodic potentials and linear part displaying Dirac points in the dispersion relation. By introducing a suitable periodic…
In the present work, we revisit the highly active research area of inhomogeneously nonlinear defocusing media and consider the existence, spectral stability and nonlinear dynamics of bright solitary waves in them. We use the anti-continuum…
Solitary waves of nonlinear Dirac, Maxwell-Dirac and Klein-Gordon-Dirac equations are considered. We prove that the energy-momentum relation for solitary waves coincides with the Einstein energy-momentum relation for point particles.
We study nonlinear bound states, or solitary waves, in the Dirac-Maxwell system proving the existence of solutions in which the Dirac wave function is of the form $\phi(x,\omega)e^{-i\omega t}$, $\omega\in(-m,\omega_*)$, with some…
We study solitary wave solutions of the fifth-order Korteweg - de Vries equation which contains, besides the traditional quadratic nonlinearity and third-order dispersion, additional terms including cubic nonlinearity and fifth order linear…
The presence of spatial inhomogeneity in a nonlinear medium restricts the formation of Solitary Waves (SW) on a discrete set of positions whereas a nonlocal nonlinearity tends to smooth the medium response by averaging over neighboring…
Peridynamics describes the nonlinear interactions in spatially extended Hamiltonian systems by nonlocal integro-differential equations, which can be regarded as the natural generalization of lattice models. We prove the existence of…
The present paper is the first part of a project devoted to the fractional nonlinear Schr\"{o}dinger (fNLS) equation. It is concerned with the existence and numerical generation of the solitary-wave solutions. For the first point, some…
We analyze the spectral and dynamical stability of solitary wave solutions to the Lugiato-Lefever equation (LLE) on $\mathbb{R}$. Our interest lies in solutions that arise through bifurcations from the phase-shifted bright soliton of the…
In this paper, we characterize a family of solitary waves for NLS with derivative (DNLS) by the structue analysis and the variational argument. Since (DNLS) doesn't enjoy the Galilean invariance any more, the structure analysis here is…
We study standing waves for the nonlinear Schr\"odinger equation on a discrete graph. We characterize for a self-adjoint realizations of Schr\"odinger operators conditions related with the geometry of the graph that guarantee discreteness…