A new integrable 3+1 dimensional generalization of the Burgers equation

Details A new integrable 3+1 dimensional generalization of the Burgers equation A new integrable 3+1 dimensional generalization of the Burgers equation

2004-11-29

arxiv.org/abs/nlin/0411061v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

8 pages

Scientific paper

A new nonlinear 3+1 dimensional evolution equation admitting the Lax pair is presented. In the case of one spatial dimension, the equation reduces to the Burgers equation. A method of construction of exact solutions, based on a class of discrete symmetries of the former equation is developed. These symmetries reduce to the Cole-Hopf transformation in one-dimensional limit. Some exact solutions are analyzed, in the physical context of spatial dissipative structures and shock wave dressing.

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