BLP dissipative structures in plane

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 reduced 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 $t\to \infty$. These solutions we call the BLP dissipative structures.

arXiv comment7 pages, AMS-TeX

References in corpus (1)

• Darboux Transformation for Dirac Equations with (1+1) potentials

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