Novel solitary patterns in a class of Klein–Gordon equations

IF 2.7 3区 数学 Q1 MATHEMATICS, APPLIED
Philip Rosenau , Slava Krylov
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引用次数: 0

Abstract

We study the emergence, stability and evolution of solitons and compactons in a class of Klein–Gordon equations uttuxx+u=u1+nκ1+2nu1+2n,1/2<n,endowed with both trivial and non-trivial stable equilibria, and demonstrate that similarly to the classical κ1+2n=0 cases, solitons are linearly unstable, but the instability weakens as κ1+2n, and vanishes at κ1+2ncrit=1+n(2+n)2, where solitons disappear and kink forms.
As the growing unstable soliton approaches the non-trivial equilibrium, it morphs into a ’mesaton’, a robust box shaped sharp pulse with a flat-top plateau, which expands at a sonic speed. In the κ1+2ncrit vicinity, where instability is suppressed, whereas the internal modes have hardly changed, solitons persist for a very long time but then, rather than turn into mesaton, convert into a breather-like formation.
Linear damping tempers the conversion and slows mesaton’s propagation. When 1/2<n<0, compactons emerge and being unstable morph either into a mesaton or into a breather-like formation.
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来源期刊
Physica D: Nonlinear Phenomena
Physica D: Nonlinear Phenomena 物理-物理:数学物理
CiteScore
7.30
自引率
7.50%
发文量
213
审稿时长
65 days
期刊介绍: Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.
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