Solutions of multidimensional PDEs representable in the form of one-dimensional flows

by Dr A. Zenchuk (Institute of problems of chemical physics, RAS, Chernogolovka, Russia)

Monday 28 Oct 2013, 15:00 → 16:00 Europe/Rome

Aula 2 (Dipartimento di Fisica - Ed. G. Marconi)

We represent an algorithm reducing an (M+1)-dimensional non linear partial differential equation (PDE) representable in the form of one-dimensional flow (u_t + w_x = 0) to the family of M-dimensional nonlinear PDEs F(u,w)=0, where F is a general (or particular) solution of a certain second order two - dimensional nonlinear PDE. In particular, the M - dimensional PDE might be an ordinary differential equation (ODE) that, in some cases, may be integrated yielding explicit solutions of the original (M+1)-dimensional equation. Moreover, a spectral parameter may be introduced into the function F, yielding a linear spectral equation associated with the original PDE. The simplest examples of nonlinear PDEs with their explicit solutions are given.