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New solitary wave solution of the combined KdV and mKdV equation. (English) Zbl 0941.35098

Summary: This paper presents two different methods for the construction of new exact solitary wave solutions to the combined KdV and mKdV equation. There exist 12 types of soliton solutions which reduce to those of the mKdV equation. There exist three types of soliton solutions which reduce to those of the KdV equation.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35C05 Solutions to PDEs in closed form
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