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Solitons in a nonlinear model medium. (English) Zbl 0754.35132
Summary: The periodic stationary solutions of a model nonlinear evolution equation simulating the propagation of short-wave perturbations in a relaxing medium are studied. Solutions expressed by a multiple-valued function are shown to exist. A method for determining the nonlinear interaction between solitary waves is suggested. An example of a collision of solitons is given.
MSC:
35Q51Soliton-like equations
35Q53KdV-like (Korteweg-de Vries) equations
82C40Kinetic theory of gases (time-dependent statistical mechanics)