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Zbl 1203.35234
Liu, Zhengrong; Ouyang, Zhengyong
A note on solitary waves for modified forms of Camassa-Holm and Degasperis-Procesi equations. (English)
[J] Phys. Lett., A 366, No. 4-5, 377-381 (2007). ISSN 0375-9601

Summary: Consider the mCH and mDP equations given by $u_t - u_{xxt}+3u^{2}u_x=2u_xu_{xx}+uu_{xxx}$, and $u_t - u_{xxt}+4u^{2}u_x=3u_xu_{xx}+uu_{xxx}$, respectively. A new characteristic of solitary wave solutions, bell-shaped solitary wave and peakon coexist for the same wave speed, is found. Previous some results are extended. A conjecture is clarified.

MSC 2000:: *35Q53 KdV-like equations
35C08

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Zentralblatt MATH Berlin [Germany]