Analytical Methods for Solving Nonlinear Partial Differential Equations

Daniel Arrigo

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English

Springer International Publishing AG
29 October 2023

Calculus & mathematical analysis; Differential calculus & equations; Applied mathematics

Series: Synthesis Lectures on Mathematics & Statistics

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.

By: Daniel Arrigo
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: Second Edition 2022
Dimensions: Height: 240mm, Width: 168mm,
Weight: 328g
ISBN: 9783031170713
ISBN 10: 3031170717
Series: Synthesis Lectures on Mathematics & Statistics
Pages: 174
Publication Date: 29 October 2023
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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

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; symmetry analysis of nonlinear PDEs; and solutions to physically important equations, such as nonlinear heat equations and governing equations modeling of granular materials and nonlinear elasticity. In 2008, Dr. Arrigo received the Oklahoma-Arkansas Section of the Mathematical Association of America’s Award for Distinguished Teaching of College or University Mathematics and in 2019 the University of Central Arkansas’s Teaching Excellence Award.