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

Rudnev, M.; Yurov, A. V.; Yurov, V. A.

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

Authors

Rudnev, M.

Yurov, A. V.

Yurov, V. A.

Description

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.
8 pages