Nonlinear dispersion relations

Authors:
A. Ludu;P. G. Kevrekidis
Affiliations:
Northwestern State University, Department of Chemistry and Physics, Natchitoches, LA 71497, USA;Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA
Venue:
Mathematics and Computers in Simulation
Year:
2007

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Propagation of sech2-type solitary waves in hierarchical KdV-type systems

Mathematics and Computers in Simulation

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Abstract

We examine how nonlinear dispersion relations (NLDR) can be used as a simple, universal algebraic tool to provide information for the localized, nonlinear solutions of PDE that model physical systems. Such scaling relations between width, amplitude and velocity are of great help for numerical investigations of nonlinear solutions. The methodology is applied to a variety of examples from diverse branches of physics, both Hamiltonian as well as dissipative ones. The limitations of the approach are also discussed.