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

M. Rudnev·A. V. Yurov·V. A. Yurov
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Abstract

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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M. Rudnev, A. V. Yurov, V. A. Yurov. 2004-11-29. A new integrable 3+1 dimensional generalization of the Burgers equation. https://arxiv.org/abs/nlin/0411061

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