Nonlinear Euler-Poisson-Darboux Equations: Initial Value Problems and Exact Solutions

This book is devoted to study multidimensional linear and nonlinear partial differential equations. Among several methods to deal with higher dimensional linear partial differential equations, the elegant method of Spherical Means has spacial importance since this method reduces the higher dimensional equations to the one dimensional radial equations of Euler-Poisson-Darboux type which are well studied. Although this method is applicable only to the linear differential equations, by some special transformations, like the Cole-Hopf transformation and the Backlaund transformation, exact solutions of multidimensional nonlinear partial differential equations of the Spherical Liouville, Sine- Gordon and Burgers type are constructed.