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Zbl 0985.37072
Li, Jibin; Liu, Zhengrong
Smooth and non-smooth traveling waves in a nonlinearly dispersive equation. (English)
[J] Appl. Math. Modelling 25, No.1, 41-56 (2000). ISSN 0307-904X

Summary: The method of the phase plane is employed to investigate the solitary and periodic traveling waves in a nonlinear dispersive integrable partial differential equation. It is shown that the existence of a singular straight line in the corresponding ordinary differential equation for traveling wave solutions is the reason that smooth solitary wave solutions converge to solitary cusp wave solutions when the parameters are varied. The different parameter conditions for the existence of different kinds of solitary and periodic wave solutions are rigorously determined.

MSC 2000:: *37K10 Completely integrable systems etc.
35Q58 Other completely integrable PDE
35B65 Smoothness of solutions of PDE
76B25 Solitary waves, etc. (inviscid fluids)
34C37 Homoclinic and heteroclinic solutions of ODE

Keywords: solitary waves; periodic waves; integrable system; bifurcations of phase portraits; smoothness of waves

Cited in: Zbl 1237.37051

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