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New sets of solitary wave solutions to the KdV, mKdV, and the generalized KdV equations. (English) Zbl 1131.35385
Summary: We introduce new schemes, each combines two hyperbolic functions, to study the KdV, mKdV, and the generalized KdV equations. It is shown that this class of equations gives conventional solitons and periodic solutions. We also show that the proposed schemes develop sets of entirely new solitary wave solutions in addition to the traditional solutions. The analysis can be used to a wide class of nonlinear evolutions equations.

35Q53KdV-like (Korteweg-de Vries) equations
37K40Soliton theory, asymptotic behavior of solutions
35C05Solutions of PDE in closed form
Full Text: DOI
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