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Symmetry, exact solutions and conservation laws of the coupled KdV equations. (Chinese. English summary) Zbl 1224.35379

Summary: By using the modified CK’s direct method, we set up a symmetry group theorem for the coupled KdV equations. Applying the theorem, some new explicit solutions of the coupled KdV equations are obtained by old solutions of the equations. Based on the results of Lie symmetries, we also get conservation laws of the coupled KdV equations.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35L65 Hyperbolic conservation laws
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