Explicit solutions of the generalized KdV equations with higher order nonlinearity. (English) Zbl 1089.35530

Summary: By constructing auxiliary functions and equations, we find some new explicit solutions of the generalized KdV equations with higher order nonlinearity. In particular, we get the peaked solitary wave solutions of the generalized KdV equations.


35Q53 KdV equations (Korteweg-de Vries equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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