
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
Abstract:
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
FitzHughNagumoSemenov and Zel'dovich equations.
Now we find new spiral wave solutions (with A.K. Volosova),
and solutions of FokkerPlanck equation (with S.O. Sinitzyn and D.V. Urchenko).
References:
[1] Volosov K.A. in Konf. "Gertsenovskie chteniya", 1722
aprelya 2006 g. (Proc. Conf. "Gertsen readings", April 1722,
2006), St. Petersburg, 2006.
[2] Volosov K.A. Construction of solutions of
quasilinear parabolic equations in parametric form. Differential
Equations2007, V. 43, N 4, p.507512.
[3] Volosov K.A. Thesis of Doctoral Dissertation in
Mathematics and Physics, MIEM, Moscow, 2007. http://eqworld.ipmnet.ru.
[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. 1114.
[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. 2939. 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", 1318 aprelya 2009 g. (Proc.
Conf. "Gertsen readings", April 1318, 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).
Presentation

