相关论文: Spectral property for the 2D Zakharov-Kuznetsov eq…
In this paper, we develop the modulation analysis, the perturbation argument and the Virial identity similar as those in \cite{MartelM:Instab:gKdV} to show the orbital instability of the solitary waves $\Q\sts{x-ct}\e^{\i\omega t}$ of the…
In this paper we establish the nonlinear stability of solitary traveling-wave solutions for the Kawahara-KdV equation $$u_t+uu_x+u_{xxx}-\gamma_1 u_{xxxxx}=0,$$ and the modified Kawahara-KdV equation $$u_t+3u^2u_x+u_{xxx}-\gamma_2…
In this work, we primarily focus on the two-phase solutions and their stability to the focusing mKdV equation. By employing the algebro-geometric approach in combination with an effective integration method, we construct explicit two-phase…
We establish the nonlinear stability of solitary waves (solitons) and periodic traveling wave solutions (cnoidal waves) for a Korteweg-de Vries (KdV) equation which includes a fifth order dispersive term. The traveling wave solutions which…
Small-amplitude waves in the Fermi-Pasta-Ulam (FPU) lattice with weakly anharmonic interaction potentials are described by the generalized Korteweg-de Vries (KdV) equation. Justification of the small-amplitude approximation is usually…
We consider the spectral problem of the Lax pair associated to periodic integrable partial differential equations. We assume this spectral problem to be a polynomial of degree $d$ in the spectral parameter $\lambda$. From this assumption,…
In this paper, we propose a class of adaptive multiresolution (also called adaptive sparse grid) ultra-weak discontinuous Galerkin (UWDG) methods for solving some nonlinear dispersive wave equations including the Korteweg-de Vries (KdV)…
In this paper, we study the long time behavior of solutions of Klein-Gordon-Zakharov system. We show that there exists a solution with special characteristics, which we shall refer to as a dipole solution, that is, there exists a solution…
We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent, and rigorous manner. The scalar…
We study strong instability (by blow-up) of the standing waves for the nonlinear Schr\"odinger equation with $\delta$-interaction on a star graph $\Gamma$. The key ingredient is a novel variational technique applied to the standing wave…
A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type…
The local and global control results for a general higher-order KdV-type operator posed on the unit circle are presented. Using spectral analysis, we are able to prove local results, that is, the equation is locally controllable and…
We consider the one-dimensional nonlinear Schr\"odinger equation with an attractive delta potential and mass-supercritical nonlinearity. This equation admits a one-parameter family of solitary wave solutions in both the focusing and…
In this work, we consider the electromechanical density pulse as a coupled solitary waves represented by a longitudinal compression wave and an out-of-plane transversal wave (i.e., perpendicular to the membrane surface). We analyzed using,…
The lattice potential Korteweg-de Vries equation (LKdV) is a partial difference equation in two independent variables, which possesses many properties that are analogous to those of the celebrated Korteweg-de Vries equation. These include…
This article addresses the study of the complex version of the modified Korteweg-de Vries equation using two different approaches. Firstly, the singular manifold method is applied in order to obtain the associated spectral problem, binary…
We report results of systematic numerical studies of 2D matter-wave soliton families supported by an external potential, in a vicinity of the junction between stable and unstable branches of the families, where the norm of the solution…
The Kadomtsev-Petviashvili (KP) nonlinear wave equation is the three dimensional generalization of the Korteveg-de Vries (KdV) equation. We show how to obtain the cylindrical KP (cKP) and cartesian KP in relativistic fluid dynamics. The…
We prove existence and stability results for a two-parameter family of solitary-wave solutions to a system in which an equation of nonlinear Schr\"odinger type is coupled to an equation of Korteweg-de Vries type. Such systems model…
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…