Nonlinear Partial Differential Equations: Techniques And Recent Developments

Prasanta Chatterjee, Kaushik Roy, Laxmikanta Mandi (Autoren)

Buch | Hardcover

416 Seiten

2025
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-98-1673-6 (ISBN)

Artikel merken

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.

Erscheinungsdatum	14.10.2025
Verlagsort	Singapore
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Naturwissenschaften ► Physik / Astronomie
ISBN-10	981-98-1673-4 / 9819816734
ISBN-13	978-981-98-1673-6 / 9789819816736
Zustand	Neuware