Related papers: Transverse instability of the CH-KP-I equation
Using a generalized framework that consists of evolution of the solution to the Camassa- Holm equation and its energy measure, we establish the global-in-time orbital stability of peakons with respect to the perturbed (energy) conservative…
In this article, we prove a uniqueness result for a coefficient inverse problems regarding a wave, a heat or a Schr\"odinger equation set on a tree-shaped network, as well as the corresponding stability result of the inverse problem for the…
The purpose of this paper is to expand the recent work of Sardar et al. [Phys. Plasmas 23, 123706 (2016)] on the existence and stability of alternative dust ion acoustic solitary wave solution of the combined modified Kadomtsev Petviashvili…
In this paper we prove the existence and the stability of small-amplitude quasi-periodic solutions with Sobolev regularity, for the 1-dimensional forced Kirchoff equation with periodic boundary conditions. This is the first KAM result for a…
The aim of this work is to establish a linear instability criterium of stationary solutions for the Korteweg-de Vries model on a star graph with a structure represented by a finite collections of semi-infinite edges. By considering a…
We study the behavior of perturbations in a compressible one-dimensional inviscid gas with an ambient state consisting of constant pressure and periodically-varying density. We show through asymptotic analysis that long-wavelength…
A defining characteristic of the Kadomstev-Petviashvili (KP) model equation is that the well-posedness results are subject to the restriction that at all transverse positions, the mass $\int u \,dx = \text{constant independent of $y$}.$ In…
In this paper, we investigate the non-autonomous discrete Kadomtsev-Petviashvili (KP) system in terms of generalized Cauchy matrix approach. These equations include non-autonomous bilinear lattice KP equation, non-autonomous lattice…
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…
The internal control problem for the Kadomstev-Petviashvili II equation, known as KP-II, is the object of study in this paper. The controllability in $L^2(T)$ from vertical strip is proved using the Hilbert Unique Method through the…
In this article, we discuss stability of the one-dimensional overdamped Lange\-vin equation in double-well potential. We determine unstable and stable equilibria, and discuss the rate of convergence to stable ones. Also, we derive…
The Petviashvili's iteration method has been known as a rapidly converging numerical algorithm for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave equations with power-law nonlinearity: \ $-Mu+u^p=0$, where…
The $b$-family of Camassa-Holm ($b$-CH) equation is a one-parameter family of PDEs, which includes the completely integrable Camassa-Holm and Degasperis-Procesi equations but possesses different Hamiltonian structures. Motivated by this, we…
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…
Dispersive PDEs are important both in applications (wave phenomena e.g. in hy- drodynamics, nonlinear optics, plasma physics, Bose-Einstein condensates,...) and a mathematically very challenging class of partial differential equations,…
The modified Kadomtsev-Petviashvili (mKP) equation is shown in this paper to be decomposable into the first two soliton equations of the 2N-coupled Chen-Lee-Liu and Kaup-Newell hierarchies by respectively nonlinearizing two sets of symmetry…
We prove new well-posedness results for dispersion-generalized Kadomtsev--Petviashvili I equations in $\mathbb{R}^2$, which family links the classical KP-I equation with the fifth order KP-I equation. For strong enough dispersion, we show…
Two-dimensional reductions of the KP-Whitham system, namely the overdetermined Whitham modulation system for five dependent variables that describe the periodic solutions of the Kadomtsev-Petviashvili equation, are studied and…
We consider a simple model for multidimensional cone-wise linear dynamics around cusp-like equilibria. We assume that the local linear evolution is either $\mathbf{v}^\prime=\mathbb{A}\mathbf{v}$ or $\mathbb{B}\mathbf{v}$ (with…
The two-dimensional cubic nonlinear Schrodinger equation admits a large family of one-dimensional bounded traveling-wave solutions. All such solutions may be written in terms of an amplitude and a phase. Solutions with piecewise constant…