On The Stability of the Compacton Solutions

Abstract

The stability of the recently discovered compacton solutions is studied by means of both linear stability analysis as well as Lyapunov stability criteria. From the results obtained it follows that, unlike solitons, all the allowed compacton solutions are stable, as the stability condition is satisfied for arbitrary values of the nonlinearity parameter. The results are shown to be true even for the higher order nonlinear dispersion equations for compactons. Some new conservation laws for the higher order nonlinear dispersion equations are also presented.

9 pages, revtex style, no figures

References in corpus (3)

• Solitary Waves and Compactons in a class of Generalized Korteweg-DeVries Equations
• Stationary Solitons of the Fifth Order KdV-type Equations and their Stabilization
• One parameter family of Compacton Solutions in a class of Generalized Korteweg-DeVries Equations

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• Dissipative perturbations for the K(n,n) Rosenau-Hyman equation
• On the properties of compacton-anticompacton collisions
• Stability of Compacton Solutions of Fifth-Order Nonlinear Dispersive Equations
• Peakompactons: Peaked compact nonlinear waves
• Localized Analytical Solutions and Parameters Analysis in the Nonlinear Dispersive Gross-Pitaevskii Mean-Field GP (m,n) Model with Space-Modulated Nonlinearity and Potential