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Generalized Kadomtsev-Petviashvili equation with an infinite-dimensional symmetry algebra. (English) Zbl 1012.35074

Summary: A generalized Kadomtsev-Petviashvili equation, describing water waves in oceans of varying depth, density and vorticity is discussed. A priori, it involves 9 arbitrary functions of one or two variables. The conditions are determined under which the equation allows an infinite-dimensional symmetry algebra. This algebra can involve up to three arbitrary functions of time. It depends on precisely three such functions if and only if it is completely integrable.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35A30 Geometric theory, characteristics, transformations in context of PDEs
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures

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References:

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