Compactons: Solitons with finite wavelength

Journal Article · Mon Feb 01 00:00:00 EST 1993 · Physical Review Letters; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.70.564· OSTI ID:7179523

Rosenau, P; Hyman, J M ^[1]

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1. Department of Mechanical Engineering, Technion, Haifa 32000 (Israel) Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States) Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

The understand the role of nonlinear dispersion in pattern formation, we introduce and study Korteweg--de Vries--like equations wtih nonlinear dispersion: [ital u][sub [ital t]]+([ital u][sup [ital m]])[sub [ital x]]+([ital u][sup [ital n]])[sub [ital x][ital x][ital x]]=0, [ital m],[ital n][gt]1. The solitary wave solutions of these equations have remarkable properties: They collide elastically, but unlike the Korteweg--de Vries ([ital m]=2, [ital n]=1) solitons, they have compact support. When two compactons'' collide, the interaction site is marked by the birth of low-amplitude compacton-anticompacton pairs. These equations seem to have only a finite number of local conservation laws. Nevertheless, the behavior and the stability of these compactons is very similar to that observed in completely integrable systems.

• OSTI ID: 7179523
• Journal Information: Physical Review Letters; (United States), Vol. 70:5; ISSN 0031-9007
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
NONLINEAR PROBLEMS
SOLITONS
PARTIAL DIFFERENTIAL EQUATIONS
AMPLITUDES
DISPERSION RELATIONS
ELASTICITY
KORTEWEG-DE VRIES EQUATION
PATTERN RECOGNITION
DIFFERENTIAL EQUATIONS
EQUATIONS
MECHANICAL PROPERTIES
QUASI PARTICLES
TENSILE PROPERTIES
661100* - Classical & Quantum Mechanics- (1992-)