相关论文: Instability of nonlinear dispersive solitary waves

We consider the linearized instability of 2D irrotational solitary water waves. The maxima of energy and the travel speed of solitary waves are not obtained at the highest wave, which has a 120 degree angle at the crest. Under the…

This paper sheds new light on the stability properties of solitary wave solutions associated with models of Korteweg-de Vries and Benjamin\&Bona\&Mahoney type, when the dispersion is very lower. Via an approach of compactness, analyticity…

We prove nonlinear modulational instability for both periodic and localized perturbations of periodic traveling waves for several dispersive PDEs, including the KDV type equations (e.g. the Whitham equation, the generalized KDV equation,…

Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schr\"odinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, that span a…

Stability of solitary waves in a thin inextensible and unshearable rod of infinite length is studied. Solitary-wave profile ofthe elastica of such a rod without torsion has the form of a planar loop and its speed depends on a tension in the…

The stability properties of line solitary wave solutions of the (2+1)-dimensional Boussinesq equation with respect to transverse perturbations and their consequences are considered. A geometric condition arising from a multi-symplectic…

We study asymptotic stability of solitary wave solutions in the one-dimensional Benney-Luke equation, a formally valid approximation for describing two-way water wave propagation. For this equation, as for the full water wave problem, the…

Frequently encountered in nature, internal solitary waves in stratified fluids are well-observed and well-studied from the experimental, the theoretical, and the numerical perspective. From the mathematical point of view, these waves are…

In this work, we systematically generalize the Evans function methodology to address vector systems of discrete equations. We physically motivate and mathematically use as our case example a vector form of the discrete nonlinear Schrodinger…

Boussinesq-type wave equations involve nonlinearities and dispersion. In this paper a Boussinesq-type equation with amplitude-dependent nonlinearities is presented. Such a model was proposed by Heimburg and Jackson (2005) for describing…

We review asymptotic stability of solitary waves for nonlinear dispersive equations set on the line. Our focus is threefold: first, the nonlinear Schrodinger equation; second, the notion of full asymptotic stability (which states that…

We study the asymptotic linear stability of a two-parameter family of solitary waves for the isothermal Euler-Poisson system. When the linearized equations about the solitary waves are considered, the associated eigenvalue problem in $L^2$…

The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…

This paper concerns spectral stability of nonlinear waves in KdV-type evolution equations. The relevant eigenvalue problem is defined by the composition of an unbounded self-adjoint operator with a finite number of negative eigenvalues and…

The extended KdV equation is a nonlinear dispersive wave model that is asymptotically or variationally derived from the full dispersive Euler shallow water waves equations when gravity-capillary and higher order nonlinear effects are taken…

We present a method to prove nonlinear instability of solitary waves in dispersive models. Two examples are analyzed: we prove the nonlinear long time instability of the KdV solitary wave (with respect to periodic transverse perturbations)…

We solve the Vlasov equation for the longitudinal distribution function and find stationary wave patterns when the distribution in the energy error is Maxwellian. In the long wavelength limit a stability criterion for linear waves has been…

In recent work, Baird et al. have introduced a generalized Maslov index which allows oscillation techniques that have previously been restricted to eigenvalue problems with underlying Hamiltonian structure to be extended to the…

The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros…

We study by a combination of numerical and analytical Evans function techniques the stability of solitary wave solutions of the St. Venant equations for viscous shallow-water flow down an incline, and related models. Our main result is to…