Nonlinear Klein-Gordon soliton mechanics

Journal Article · Tue Nov 10 04:00:00 EST 1992 · International Journal of Modern Physics B; (United States)

DOI:https://doi.org/10.1142/S021797929200150X· OSTI ID:6731431

Reinisch, G ^[1]

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1. CNRS: U.R.A. 1279, Equipe de Dynamique Nonlineaire des Milieux Continus, 14, rue de la Vigne, F-06430 Tende (France)

Nonlinear Klein-Gordon solitary waves - or solitons in a loose sense - in n+1 dimensions, driven by very general external fields which must only satisfy continuity - together with regularity conditions at the boundaries of the system, obey a quite simple equation of motion. This equation is the exact generalization to this dynamical system of infinite number of degrees of freedom - which may be conservative or not - of the second Newton's law setting the basis of material point mechanics. In the restricted case of conservative nonlinear Klein-Gordon systems, where the external driving force is derivable from a potential energy, we recover the generalized Ehrenfest theorem which was itself the extension to such systems of the well-known Ehrenfest theorem in quantum mechanics. This review paper first displays a few (of one-dimensional sine-Gordon type) typical examples of the basic difficulties related to the trial construction of solitary-waves is proved and the derivation of the previous sine-Gordon examples from this theorem is displayed. Two-dimensional nonlinear solitary-wave patterns are considered, as well as a special emphasis is put on the applications to space-time complexity of 1-dim. sine-Gordon systems.

• OSTI ID: 6731431
• Journal Information: International Journal of Modern Physics B; (United States), Journal Name: International Journal of Modern Physics B; (United States) Vol. 6:21; ISSN IJPBEV; ISSN 0217-9792
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
DOCUMENT TYPES
ENERGY
EQUATIONS
EQUATIONS OF MOTION
FIELD EQUATIONS
ITERATIVE METHODS
KLEIN-GORDON EQUATION
MECHANICS
NEWTON METHOD
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIAL ENERGY
QUANTUM MECHANICS
QUASI PARTICLES
REVIEWS
SINE-GORDON EQUATION
SOLITONS
SPACE-TIME
TWO-DIMENSIONAL CALCULATIONS
USES
WAVE EQUATIONS