On solving problems in the mechanics of solids and fluids by a generalized method of characteristics (Q1097732)

A generalized method of characteristics is used to find solutions to nonlinear problems in the mechanics of solids and fluids. Applicability of the method of partial differential equations of higher order is demonstrated by constructing solutions to the Korteweg-de Vries equation, including soliton and centered wave solutions. Systems of two, first order, nonlinear partial differential equations with two independent variables are solved in order to demonstrate the applicability of the method in such cases. A single, first order partial differential equation need not be treated since the generalized method of characteristics has been shown to reduce to the classical method in this case [see the author, An order independent method of characteristics for solving partial differential equations (in press)]. We conclude with the construction of generalized characteristic solutions to the equations of antiplane, isotropic, power-law creep (i.e. nonlinear systems with three independent and three dependent variables).