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Zbl 1027.35115
Wazwaz, A.M.
Exact special solutions with solitary patterns for the nonlinear dispersive $K(m,n)$ equations.
(English)
[J] Chaos Solitons Fractals 13, No.1, 161-170 (2002). ISSN 0960-0779

Summary: We study the genuinely nonlinear dispersive $K(m,n)$ equation, $$u_t-(u^m)_x+ (u^n)_{xxx}=0,$$ which exhibits solutions with solitary patterns. Exact solutions that create solitary patterns having cusps or infinite slopes are developed. The nonlinear equation $K(m,n)$ is addressed for two different cases, namely when $m=n=\text{odd}$ integer and when $m=n=\text {even}$ integer. General formulas for the solutions of these cases of the $K(m,n)$ equations are established.
MSC 2000:
*35Q53 KdV-like equations
35Q51 Solitons
35K57 Reaction-diffusion equations

Keywords: soliton

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