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New exact solitary-wave solutions for the \(K(2, 2, 1)\) and \(K(3, 3, 1)\) equations. (English) Zbl 1137.35427
Summary: \(K(2, 2, 1)\) equation: \(u_t + (u^{2})_x - (u^{2})_{xxx} + u_{5x} = 0\) and \(K(3, 3, 1)\) equation: \(u_t + (u^{3})_x - (u^{3})_{xxx} + u_{5x} = 0\) are investigated. New exact solitary solutions are developed by using the decomposition method and the symbolic computation system Maple.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
35-04 Software, source code, etc. for problems pertaining to partial differential equations
Software:
Maple
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Full Text: DOI
References:
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