Analytical Methods for Solving Nonlinear Partial Differential Equations - Arrigo, Daniel

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Résumé :
This textbook provides an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PDEs drawn from science and engineering, readers are introduced to techniques to obtain exact solutions of NLPDEs. The chapters include the following topics: Nonlinear PDEs are Everywhere; Differential Substitutions; Point and Contact Transformations; First Integrals; and Functional Separability. Readers are guided through these chapters and are provided with several detailed examples. Each chapter ends with a series of exercises illustrating the material presented in each chapter. This Second Edition includes a new method of generating contact transformations and focuses on a solution method (parametric Legendre transformations) to solve a particular class of two nonlinear PDEs.

Biographie:
Daniel Arrigo earned his PhD from the Georgia Institute of Technology in 1991. He has been on staff in the Department of Mathematics at the University of Central Arkansas since 1999 and is currently Professor of Mathematics. He has published over 30 journal articles and three books. His research interests include the construction of exact solutions of PDEs...

Sommaire:
Nonlinear PDEs are Everywhere.- Differential Substitutions.- Point and Contact Transformations.- First Integrals.- Functional Separability.