Stability of Nonlinear Waves Resonantly Sustained

Abstract

This talk will examine the stability properties of representative cases of nonlinear dispersive waves generated and sustained at resonance of physical systems capable of supporting solitary waves. The criteria are sought for realizing the remarkable phenomenon of periodic production of upstream-radiating solitary waves by critical disturbances moving steadily in a layer of shallow water as modeled by the forced KdV equation. Of primary interest are the distinctive features of instabilities of a few typical steady basic flows, the salient new characteristics of the associated eigenvalue problems, the relevant nonlinear effects, and the resulting bifurcation diagrams.

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