Analytical Methods for Solving Nonlinear Partial Differential Equations

This is a university-level textbook for readers who want to find exact solutions to nonlinear partial differential equations. It opens by presenting a range of these equations drawn from science and engineering, so readers can see where such problems come from before any solution methods are introduced.

The book is organised into five chapters. The first shows how widespread nonlinear PDEs are in practice. The remaining chapters cover differential substitutions, point and contact transformations, first integrals, and functional separability. The author takes readers step by step through each technique with a number of detailed worked examples, and every chapter closes with exercises that reinforce the material.

This second edition adds a new approach to generating contact transformations. It also concentrates on parametric Legendre transformations, a solution method for one particular class of two nonlinear PDEs.