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Analytical Methods for Solving Nonlinear Partial Differential Equations [electronic resource] / by Daniel Arrigo.

By: Arrigo, Daniel [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Synthesis Lectures on Mathematics & Statistics: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2022Edition: 2nd ed. 2022.Description: XII, 174 p. 3 illus., 2 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783031170690.Subject(s): Differential equations | Mathematics | Mathematical analysis | Differential Equations | Mathematics | Analysis | Applications of MathematicsAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 515.35 Online resources: Click here to access online
Contents:
Nonlinear PDEs are Everywhere -- Differential Substitutions -- Point and Contact Transformations -- First Integrals -- Functional Separability. .
In: Springer Nature eBookSummary: 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. In addition, this book: Presents analytical methods to solve nonlinear partial differential equations (NLPDEs) Includes techniques for solving first and second order NLPDEs and provides interdisciplinary examples Contains numerous exercises throughout to facilitate learning and has been class tested over the past 10 years.
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Nonlinear PDEs are Everywhere -- Differential Substitutions -- Point and Contact Transformations -- First Integrals -- Functional Separability. .

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. In addition, this book: Presents analytical methods to solve nonlinear partial differential equations (NLPDEs) Includes techniques for solving first and second order NLPDEs and provides interdisciplinary examples Contains numerous exercises throughout to facilitate learning and has been class tested over the past 10 years.

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