Soliton evolution and radiation loss for the Korteweg--de Vries equation
- Department of Engineering Sciences and Applied Mathematics, McCormick School of Engineering, Northwestern University, Evanston, Illinois 60208 (United States) Department of Mathematics and Statistics, University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh EH93JZ, Scotland (United Kingdom)
The time-dependent behavior of solutions of the Korteweg--de Vries (KdV) equation for nonsoliton initial conditions is considered. While the exact solution of the KdV equation can in principle be obtained using the inverse scattering transform, in practice it can be extremely difficult to obtain information about a solution's transient evolution by this method. As an alternative, we present here an approximate method for investigating this transient evolution which is based upon the conservation laws associated with the KdV equation. Initial conditions which form one or two solitons are considered, and the resulting approximate evolution is found to be in good agreement with the numerical solution of the KdV equation. Justification for the approximations employed is also given by way of the linearized inverse scattering solution of the KdV equation. In addition, the final soliton state determined from the approximate equations agrees very well with the final state determined from the exact inverse scattering transform solution.
- OSTI ID:
- 6702122
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Vol. 51:1; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
KORTEWEG-DE VRIES EQUATION
SOLITONS
CONSERVATION LAWS
ENERGY LOSSES
INVERSE SCATTERING PROBLEM
TRANSIENTS
WAVE PROPAGATION
DIFFERENTIAL EQUATIONS
EQUATIONS
LOSSES
PARTIAL DIFFERENTIAL EQUATIONS
QUASI PARTICLES
661300* - Other Aspects of Physical Science- (1992-)