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Group analysis of KdV-Burgers-Kuramoto equation — allowed transformations and symmetry groups. (Chinese. English summary) Zbl 1212.35436

Summary: The allowed transformations of the variable coefficient KdV-Burgers-Kuramoto (VCKdVBK) equation \(u_t+f (x,t)uu_x+g (x, t)u_{xx}+h (x, t)u_{xxx}+k (x, t)u_{xxxx}=0\) are obtained, which leave the form invariant but possibly change the coefficients \(f, g, h\) and \(k\). Based on the different types of the allowed transformations, seven types of equivalence classes are found. Finally, Lie point symmetry groups of the VCKdVBK equation are also given.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
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