BLP dissipative structures in plane |
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| Institution: | 1. Department of Mathematics and Center of Nonlinear Equations, China University of Mining and Technology, Xuzhou, 221116, People''s Republic of China;2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, United Kingdom;1. Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs''ka Str., 01024 Kyiv, Ukraine;2. Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, A-1090 Wien, Austria;3. Department of Mathematics and Statistics, University of Cyprus, Nicosia CY 1678, Cyprus |
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| Abstract: | We study the Darboux and Laplace transformations for the Boiti–Leon–Pempinelli equations (BLP). These equations are the (1+2) generalization of the sinh-Gordon equation. In addition, the BLP equations reduce to the Burgers (and anti-Burgers) equation in a one-dimensional limit. Localized nonsingular solutions in both spatial dimensions and (anti) `blow-up' solutions are constructed. The Burgers equation's `dressing' procedure is suggested. This procedure allows us to construct such solutions of the BLP equations which are reduced to the solutions of the dissipative Burgers equations when t→∞. These solutions we call the BLP dissipative structures. |
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