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Wu, Xianbin; Rui, Weiguo; Hong, Xiaochun

Exact traveling wave solutions of explicit type, implicit type, and parametric type for \(K(m, n)\) equation. (English) Zbl 1251.35138

J. Appl. Math. 2012, Article ID 236875, 23 p. (2012).
Summary: By using the integral bifurcation method, we study the nonlinear \(K(m, n)\) equation for all possible values of \(m\) and \(n\). Some new exact traveling wave solutions of explicit type, implicit type, and parametric type are obtained. These exact solutions include peculiar compacton solutions, singular periodic wave solutions, compacton-like periodic wave solutions, periodic blowup solutions, smooth soliton solutions, and kink and antikink wave solutions. The great parts of them are different from the results in existing references. In order to show their dynamic profiles intuitively, the solutions of \(K(n, n)\), \(K(2n - 1, n)\), \(K(3n - 2, n)\), \(K(4n - 3, n)\), and \(K(m, 1)\) equations are chosen to illustrate with the concrete features.

Cited in 4 Documents

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
35C07 Traveling wave solutions
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\textit{X. Wu} et al., J. Appl. Math. 2012, Article ID 236875, 23 p. (2012; Zbl 1251.35138)
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References:

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