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Regular Seminar Vladimir Matveev (Univ. Bourgogne)
The cylindrical Kadomtsev-Petviashvily equation (CKP) also known as Johnson equation was introduced by R.S. Johnson in 1978 in the context of describing surface waves in a shallow imcopressible fluid. Later it was derived also as describing the internal waves in a stratified medium by V.D. Lipowskij in 1995. The same equation was obtained in 2000 for description of nonlinear acoustic waves by S. Leble and A. Sukhov. We present a large families of explicit solutions to the CKP-I equation and the CKP -II equation obtained by means of the algebrogeometrical approach and by use of the Darboux transformation method. Some plots of these solutions will be also presented as well as the hamiltonian formulation of the CKP model. Particular case of the obtained solutions with crossed parabolic profiles correspond well enough to the real waves observed in thin films of shallow water being cooled along the inclined plane. This talk is based on a recent joint work with A.O Smirnov and Ch. Klein.