Related papers: Solitary waves in the complementary generalized AB…
We study the long-time behavior of small and large solutions to a broad class of nonlinear Dirac-type equations. Our results are classified in 1D massless and massive cases, 3D general and $n$ dimensional in generality. In the 1D massless…
An analytical approach is proposed to study the two-photon, two-mode and intensity-dependent Rabi models. By virtue of the su(1,1) Lie algebra, all of them can be unified to the same Hamiltonian with $\mathcal{Z}_2$ symmetry. There exist…
Three (2+1)-dimensional equations, they are KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same KdV equation by different transformation of variables respectively. Since the single solitary wave…
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 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 consider a non-Abelian gauge theory in R^{4} equipped with the Minkowski metric, which provides a model for the interaction between a bosonic matter field and a gauge field with gauge group SU(2). We prove the existence of solitary waves…
We prove the existence of a $L^2$-normalized solitary wave solution for the Maxwell-Dirac equations in (3+1)-Minkowski space. In addition, for the Coulomb-Dirac model, describing fermions with attractive Coulomb interactions in the…
We explore a prototypical two-dimensional model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral stability analysis,…
Parametric simultaneous solitary wave (simulton) excitations are shown possible in nonlinear lattices. Taking a one-dimensional diatomic lattice with a cubic potential as an example we consider the nonlinear coupling between the upper…
The Calogero model bears, in the continuum limit, collective excitations in the form of density waves and solitary modulations of the density of particles. This sector of the spectrum of the model was investigated, mostly within the…
Motivated by recent progress in trapping Bose-Einstein condensed atoms in toroidal potentials, we examine solitary-wave solutions of the nonlinear Schr\"odinger equation subject to periodic boundary conditions. When the circumference of the…
In this paper, we study the existence and {multiplicity} of nontrivial solitary waves for the generalized Kadomtsev-Petviashvili equation with prescribed {$L^2$-norm} \begin{equation*}\label{Equation1} \left\{\begin{array}{l} \left(-u_{x…
The Degasperis - Procesi (DP) equation describing the propagation of shallow water waves contains a physical parameter $\omega$, and it is well-known that the DP equation admits solitary waves with a peaked crest when $\omega = 0$. In this…
In this paper, we investigate the existence and limit behaviours of travelling solitary waves of the form $\psi(t,x)=e^{i\lambda t}\varphi\left(x-vt\right)$ to the nonlinear pseudo-relativistic Schr\"odinger equation \[ i\partial_t…
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…
We present trapped solitary wave solutions of a coupled nonlinear Schr\"odinger system in $1$+$1$ dimensions in the presence of an external, supersymmetric and complex $\mathcal{PT}$-symmetric potential. The Schr\"odinger system this work…
We consider the simplest instabilities involving multiple unstable electrostatic plasma waves corresponding to four-dimensional systems of mode amplitude equations. In each case the coupled amplitude equations are derived up to third order…
In this paper, we first consider the Rosenau equation with the quadratic nonlinearity and identify its Lie symmetry algebra. We obtain reductions of the equation to ODEs, and find periodic analytical solutions in terms of elliptic…
A two-component Bose-Einstein condensate that is confined in a one-dimensional ring potential supports solitary-wave solutions, which we evaluate analytically. The derived solutions are shown to be unique. The corresponding dispersion…
We show the existence, regularity and analyticity of solitary waves associated to the following equation \begin{eqnarray*} (u_t+u^{p}u_x+ \mathcal H\partial_x^2u+ \lambda \mathcal H\partial_y^2u)_x +\mu u_{yy}=0, \end{eqnarray*} where…