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A study on KdV and Gardner equations with time-dependent coefficients and forcing terms. (English) Zbl 1202.35266
Summary: We study the KdV equation and the Gardner equation with time-dependent coefficients and forcing term for each equation. A generalized wave transformation is used to convert each equation to a homogeneous equation. The soliton ansatz is applied to the homogeneous equations to obtain soliton solutions.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35A30 Geometric theory, characteristics, transformations in context of PDEs
35C08 Soliton solutions
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