New classes of exact solutions to general nonlinear equations and systems of equations in mathematical physics. (English. Russian original) Zbl 1217.35166

Polyanin, A. D.

Dokl. Math. 78, No. 1, 607-611 (2008); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 421, No. 6, 744-748 (2008).

From the text: New classes of exact solutions to some general nonlinear equations and systems of equations of mathematical physics are described that involve arbitrary functions. Special attention is given to equations and systems of equations encountered in the theory of mass and heat transfer, mathematical biology, and wave theory.
In this paper, an exact solution is regarded in the sense of the definition given in [A. D. Polyanin, V. F. Zaitsev and A. I. Zhurov, Methods for solving nonlinear equations in mathematical physics and mechanics. Fizmatlit, Mowcow, (2005)], page 10.

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
35Q79	PDEs in connection with classical thermodynamics and heat transfer
35Q92	PDEs in connection with biology, chemistry and other natural sciences
35C05	Solutions to PDEs in closed form
80A20	Heat and mass transfer, heat flow (MSC2010)
35A24	Methods of ordinary differential equations applied to PDEs

Keywords:

reaction-diffusion equations; mass transfer; heat transfer; mathematical biology; exact solutions

References:

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