Publication: Generalized Kadomtsev–Petviashvili equation with an infinite-dimensional symmetry algebra
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Elsevier BV
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Abstract
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.
AMSLaTeX, 16 pages, no figures, corrected some typos and added two new sections
AMSLaTeX, 16 pages, no figures, corrected some typos and added two new sections
Description
Journal or Series
Journal of Mathematical Analysis and Applications
ISSN
0022-247X
ISBN
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OPEN
Keywords
Nonlinear Sciences - Exactly Solvable and Integrable Systems, Applied Mathematics, generalized Kadomtsev-Petviashvili equation, completely integrable, FOS: Physical sciences, Mathematical Physics (math-ph), KdV equations (Korteweg-de Vries equations), Kac-Moody algebra, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures, symmetry algebra, Exactly Solvable and Integrable Systems (nlin.SI), Hamiltonian structures, symmetries, variational principles, conservation laws, Analysis, Mathematical Physics, Geometric theory, characteristics, transformations in context of PDEs, vorticity