Kinks in the presence of rapidly varying perturbations

Journal Article · Sun May 01 04:00:00 EDT 1994 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.49.4542· OSTI ID:7281282

Kivshar, Y S ^[1]; Gronbech-Jensen, N ^[2]; Parmentier, R D ^[3]

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1. Optical Sciences Centre, Australian National University, Australian Capital Territory 0200, Canberra (Australia)
2. Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
3. Dipartimento di Fisica,Universita di Salerno, I-84081 Salerno (Italy)

The dynamics of sine-Gordon kinks in the presence of rapidly varying periodic perturbations of different physical origins is described analytically and numerically. The analytical approach is based on asymptotic expansions, and it allows one to derive, in a rigorous way, an effective nonlinear equation for the slowly varying field component in any order of the asymptotic procedure as expansions in the small parameter [omega][sup [minus]1], [omega] being the frequency of the rapidly varying ac driving force. Three physically important examples of such a dynamics, i.e., kinks driven by a direct or parametric ac force, and kinks on a rotating and oscillating background, are analyzed in detail. It is shown that in the main order of the asymptotic procedure the effective equation for the slowly varying field component is [ital a] renormalized sine[minus]Gordon equation in the case of the direct driving force or rotating (but phase locked to an external ac force) background, and it is [ital the] [ital double] [ital sine]-[ital Gordon] [ital equation] for the parametric driving force. The properties of the kinks described by the renormalized nonlinear equations are analyzed, and it is demonstrated analytically and numerically which kinds of physical phenomena may be expected in dealing with the renormalized, rather than the unrenormalized, nonlinear dynamics. In particular, we predict several qualitatively new effects which include, e.g., the perturbation-induced internal oscillations of the 2[pi] kink in a parametrically driven sine-Gordon model, and the generation of kink motion by a pure ac driving force on a rotating background.

• OSTI ID: 7281282
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 49:5; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

661000* -- General Physics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
ASYMPTOTIC SOLUTIONS
DYNAMICS
EQUATIONS
FIELD EQUATIONS
MECHANICS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PERTURBATION THEORY
QUASI PARTICLES
RENORMALIZATION
SERIES EXPANSION
SINE-GORDON EQUATION
SOLITONS