Nonlinear Partial Differential Equations: Techniques And Recent Developments

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Prasanta Chatterjee (Visva-bharati University, India) Kaushik Roy (Beluti Mkm High School, India)

Nonlinear Partial Differential Equations

Techniques And Recent Developments

Prasanta Chatterjee (Visva-bharati University, India), Kaushik Roy (Beluti Mkm High School, India), Laxmikanta Mandi (Gour Banga University, India)

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English

World Scientific Publishing Co Pte Ltd
09 October 2025

Differential calculus & equations; Mathematical physics

Summary
Details

This book charts a clear and systematic roadmap for nonlinear partial differential equations (NLPDES). Beginning from the definition of a partial differential equation to the recent developments of nonlinear partial differential equations, this book will be a valuable resource for advanced postgraduate students and researchers in applied mathematics, physics, nonlinear optics, and other engineering disciplines where knowledge of nonlinear differential equations is a must.

The book begins with an introductory chapter that briefly describes the developments of linear as well as nonlinear partial differential equations. Several nonlinear partial differential equations that have emerged in various fields have also been discussed. Chapter 2 introduces several analytical techniques, including the traveling wave solutions and the similarity solutions of the nonlinear partial differential equations. In Chapter 3, approximate analytical solutions and semi-analytic solutions are presented, in which solutions of non-integrable or non-autonomous nonlinear partial differential equations are investigated after suitable approximation. Some recent breakthroughs in semi-analytical approaches such as the Variational iteration method (VIM), Adomian decomposition method (ADM), Homotopy Analysis method (HAM), and Homotopy Perturbation method (HPM) are also explained with examples. Chapter 4 deals with modern advancements in NLPDE, Painlevé tests, the Inverse Scattering Method, the Lax Pair Method, Darboux Transformation, Bäcklund Transformation, and the Hirota Direct Method. The focus of this comprehensive monograph is to check the integrability and find analytical solutions for important NLPDEs according to recent developments.

By: Prasanta Chatterjee (Visva-bharati University India), Kaushik Roy (Beluti Mkm High School, India), Laxmikanta Mandi (Gour Banga University, India)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
ISBN: 9789819816736
ISBN 10: 9819816734
Pages: 416
Publication Date: 09 October 2025
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Active