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On Bäcklund transformation for a generalized Burgers equation and solitonic solutions. (English) Zbl 0944.37045
Summary: By the application of the truncated Painlevé expansion and symbolic computation method, the authors show that Bäcklund transformations exist for a generalized Burgers equation of the form \(u_t+b(t)uu_x+a(t)u_{xx}=0\) with some constraints. Kink-type solitonic solutions are found.

MSC:
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35Q53 KdV equations (Korteweg-de Vries equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35B41 Attractors
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