Related papers: Two-component vector breather solution of the modi…
We consider damped and forced discrete nonlinear Schr\"odinger equations on the lattice $\mathbb{Z}$. First we establish the existence of periodic and quasiperiodic breather solutions for periodic and quasiperiodic driving, respectively.…
Under investigation is a new (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. The main results are listed as follows: (i) lump solutions; (ii) Interaction solutions between lump wave and solitary waves; (iii) Interaction solutions…
We present new solutions to the nonautonomous nonlinear Schroedinger equation that may be realized through convenient manipulation of Bose-Einstein condensates. The procedure is based on the modulation of breathers through an analytical…
We predict that oblique breathers can be generated by a flow of two-component Bose-Einstein condensate past a polarized obstacle which attracts one component of the condensate and repels the other one. The breather exists if intra-species…
A simple model of a polymer is considered: a chain of (different) point masses, connected by harmonic springs, embedded in two dimensional space. In order to determine conditions for existence and stability of breather excitations, the…
We present in detail the implementation of the Blaizot-M\'endez-Wschebor (BMW) approximation scheme of the nonperturbative renormalization group, which allows for the computation of the full momentum dependence of correlation functions. We…
From a unified vision of vector valued solutions in weighted Banach spaces, this manuscript establishes the existence and uniqueness for space homogeneous Boltzmann bi-linear systems with conservative collisional forms arising in complex…
The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schr\"odinger equations, which incorporate the cross-phase modulation,…
The Benjamin-Ono (BO) equation describes long internal waves of small amplitude in deep fluids. Compared to its counterpart for shallow fluids, the Korteweg-de Vries (KdV) equation, the BO equation admits exact solutions for the traveling…
The generalized Benjamin-Bona-Mahony equation (gBBM) is a model for nonlinear dispersive waves which, in the long-wave limit, is approximately equivalent to the generalized Korteweg-de Vries equation (gKdV). While the long-time behaviour of…
We consider the quintic generalized Benjamin-Bona-Mahony equation $$ u_t-u_{xxt} + \partial_x\big(u + u^{5}\big)= 0,\qquad (t,x)\in \mathbb{R}_+ \times \mathbb{R}. $$ Using the space-time resonance method, we prove that sufficiently small…
The sixteen-component, no-pair Dirac--Coulomb--Breit equation, derived from the Bethe--Salpeter equation, is solved in a variational procedure using Gaussian-type basis functions for the example of positronium, muonium, hydrogen atom, and…
A hybrid lattice Boltzmann method (LBM) for binary mixtures based on the free-energy approach is proposed. Non-ideal terms of the pressure tensor are included as a body force in the LBM kinetic equations, used to simulate the continuity and…
The Buckley-Leverett equation for two phase flow in a porous medium is modified by including a dependence of capillary pressure on the rate of change of saturation. This model, due to Gray and Hassanizadeh, results in a nonlinear…
We examine the effect of dissipation on traveling waves in nonlinear dispersive systems modeled by Benjamin- Bona- Mahony (BBM)-like equations. In the absence of dissipation the BBM-like equations are found to support soliton and…
Medium modification of scattering properties in interacting Bose systems are considered by solving the Bethe-Salpeter equation. An equation of state for the normal phase (generalized Beth-Uhlenbeck formula) is given using the in-medium…
Modulational instability has been used to explain the formation of breather and rogue waves qualitatively. In this paper, we show modulational instability can be used to explain the structure of them in a quantitative way. We develop a…
We study one particular asymptotic behaviour of a solution of the fractional modified Korteweg-de Vries equation (also known as the dispersion generalised modified Benjamin-Ono equation): \begin{align}\tag{fmKdV} \partial_t u + \partial_x…
Two different versions of cubic sixth-order generalised Boussinesq-type wave equations are considered in this study. A generalised perturbation reduction method is used to solve these equations, which allows the reduction of considered…
In this series of papers, we investigate coupled systems arising in the study of two-component Bose--Einstein condensates, and we establish classification results for solutions of De Giorgi conjecture type. In the first paper of the series,…