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How to find solutions, Lie symmetries, and conservation laws of forced Korteweg-de Vries equations in optimal way. (English) Zbl 1253.35151
Summary: It is shown that the forced Korteweg-de Vries (KdV) equation studied in the recent papers [A. H. Salas, Nonlinear Anal., Real World Appl. 12, No. 2, 1314–1320 (2011; Zbl 1206.35222)] and [M. L. Gandarias and M. S. Bruzón, Nonlinear Anal., Real World Appl. 13, No. 6, 2692–2700 (2012; Zbl 1268.35106)] is reduced to the classical (constant-coefficient) KdV equation by point transformations for all values of variable coefficients. The equivalence-based approach proposed in [R. O. Popovych and O. O. Vaneeva, Commun. Nonlinear Sci. Numer. Simul. 15, No. 12, 3887–3899 (2010; Zbl 1222.35009)] allows one to obtain more results in a much simpler way.

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