Symmetries and form-preserving transformations of one-dimensional wave equations with dissipation

Abstract

General results are given for the forms of infinitesimal point symmetries of the class of partial differential equations in which utt is a function of x,t,u,ut and the x-derivatives of u up to order n ≥ 2. Continuous and discrete symmetries are then studied for the more restricted, but wide, class of equations of the form utt + K(u)ut = (F(u)ux)x + H(u)ux, F(u) ≠ 0, representing a class of one-dimensional non-linear wave equations with dissipation. A full classification of the groups of continuous point symmetries is given. In addition, new discrete point symmetries are found as well as new transformations which relate equations with different F, H and K. © 2001 Elsevier Science Ltd.