Symmetry in Nonlinear Mathematical Physics - 2009

Konstantin Volosov (Moscow State University of Railway Engineering, Russia)

New property of PDE and exact solutions in parametric form

In the present work, we suggest a new method for constructing closed formulas for exact solutions of PDE. We deal with an effective construction of the solution in a new way. In [1]-[5] a new property of PDE was found. There was construction of new solutions of Fitz-Hugh-Nagumo-Semenov and Zel'dovich equations. Now we find new spiral wave solutions (with A.K. Volosova), and solutions of Fokker-Planck equation (with S.O. Sinitzyn and D.V. Urchenko).

[1] Volosov K.A. in Konf. "Gertsenovskie chteniya", 17-22 aprelya 2006 g. (Proc. Conf. "Gertsen readings", April 17-22, 2006), St. Petersburg, 2006.
[2] Volosov K.A. Construction of solutions of quasilinear parabolic equations in parametric form. Differential Equations-2007, V. 43, N 4, p.507-512.
[3] Volosov K.A. Thesis of Doctoral Dissertation in Mathematics and Physics, MIEM, Moscow, 2007.
[4] Volosov K.A. Doklady Mathematics, Implicit Formulas for Exact Solutions of Quasilinear Partial Differential Equations. Pleiades Publishing, Ltd., 2008. In Russian in Doklady Akademii Nauk, 2008, V. 418, No. 1, pp. 11-14.
[5] Volosov K.A. Construction of Exact Solutions of Quasilinear Parabolic Equations in Parametric Form. Sibirskiy journal industrialnoy mathematiky, 2008, V. 11, N. 2(34), pp. 29-39. English translation in J. of Applied and Industrial Math.
[6] Volosova A.K., Volosov K.A., Sinitzyn S.O., Bratus A.S. in Konf. "Gertsenovskie chteniya", 13-18 aprelya 2009 g. (Proc. Conf. "Gertsen readings", April 13-18, 2009), St. Petersburg, 2009.

This is joint work with A.K. Volosova, S.O. Sinitzyn (Moscow State University of Railway Engineering, Russia) and D.V. Urchenko (St.Petersburg State Polytechnical University, Russia).