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High-frequency soliton-like waves in a relaxing medium. (English) Zbl 0946.35094
Summary: A nonlinear evolution equation is suggested to describe the propagation of waves in a relaxing medium. It is shown that in the low-frequency approach this equation is reduced to the KdVB equation. The high-frequency perturbations are described by a new nonlinear equation. This equation has ambiguous looplike solutions. It is established that a dissipative terrn, with a dissipation parameter less than some limit value, does not destroy these looplike solutions.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
74A25 Molecular, statistical, and kinetic theories in solid mechanics
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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