A note on the extension of the polar decomposition for the multidimensional Burgers equation

Details A note on the extension of the polar decomposition for the multidimensional Burgers equation A note on the extension of the polar decomposition for the multidimensional Burgers equation

2002-05-22

arxiv.org/abs/nlin/0205049v3

Phys. Rev. E vol. 67, 067301-3 (2003)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

3 pages; minor formatting and typos corrected. Submitted to Phys. Rev. E (Rapid Comm.)

Scientific paper

10.1103/PhysRevE.67.067301

It is shown that the generalizations to more than one space dimension of the pole decomposition for the Burgers equation with finite viscosity and no force are of the form u = -2 viscosity grad log P, where the P's are explicitly known algebraic (or trigonometric) polynomials in the space variables with polynomial (or exponential) dependence on time. Such solutions have polar singularities on complex algebraic varieties.

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