Instability of nonlinear dispersive solitary waves
نویسنده
چکیده
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 criteria for the existence of exponentially growing solutions to the linearized problem. The novelty is that we dealt with models with nonlocal dispersive terms, for which the spectra problem is out of reach by the Evans function technique. For the proof, we reduce the linearized problem to study a family of nonlocal operators, which are closely related to properties of solitary waves. A continuation argument with a moving kernel formula is used to find the instability criteria. These techniques have also been extended to study instability of periodic waves and of the full water wave problem. © 2008 Elsevier Inc. All rights reserved.
منابع مشابه
Transverse nonlinear instability for two-dimensional dispersive models
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) under a KP-I flow and the transverse nonlinear instability of solitary waves for the cubic nonlinear Schrödinger equation.
متن کاملInstability of Solitary Waves for a Nonlinearly Dispersive Equation
Solitary-wave solutions of a nonlinearly dispersive evolution equation are considered. It is shown that these waves are unstable in a certain parameter range.
متن کاملStability of Solitary Waves for a Nonlinearly Dispersive Equation
Solitary-wave solutions of a nonlinearly dispersive equation are considered. It is found that solitary waves are peaked or smooth waves, depending on the wave speed. The stability of the smooth solitary waves also depends on the wave speed. Orbital stability is proved for some wave speeds, while instability is proved for others.
متن کاملStability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-bona-mahony Type
This paper concerns the orbital stability and instability of solitary waves of the system of coupling equations of Benjamin-Bona-Mahony type. By applying the abstract results of Grillakis, Shatah and Strauss and detailed spectral analysis, we obtain the existence and stability of the solitary waves.
متن کاملMultilump Symmetric and Nonsymmetric Gravity-Capillary Solitary Waves in Deep Water
Multilump gravity-capillary solitary waves propagating in a fluid of infinite depth are computed numerically. The study is based on a weakly nonlinear and dispersive partial differential equation (PDE) with weak variations in the spanwise direction, a model derived by Akers and Milewski [Stud. Appl. Math., 122 (2009), pp. 249–274]. For a two-dimensional fluid, this model agrees qualitatively we...
متن کامل