Solitary waves with damped oscillatory tails: An analysis of the fifth- order Korteweg-de Vries equation. (English) Zbl 0824.35113
Summary: We construct oscillatory solitary wave solutions of a fifth-order Korteweg-de Vries equation, where the oscillations decay at infinity. These waves arise as a bifurcation from the linear dispersion curve at that wavenumber where the linear phase speed and group velocity coincide. Our approach is a wave-packet analysis about this wavenumber which leads in the first instance to a higher-order nonlinear Schrödinger equation, from which we then obtain the steady solitary wave solution. We then describe a complementary normal-form analysis which leads to the same result. In addition we derive the nonlinear Schrödinger equation for all wavenumbers, and list all the various anomalous cases.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35Q51 | Soliton equations |
| 35B32 | Bifurcations in context of PDEs |
Keywords:
fifth-order Korteweg-de Vries equation; wave-packet analysis; nonlinear Schrödinger equation; normal-form analysisReferences:
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