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Analytical properties of nonlinear partial differential equationswith applications to shallow water models /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Analytical properties of nonlinear partial differential equationsAlexei Cheviakov, Peng Zhao.
Reminder of title:	with applications to shallow water models /
Author:	Cheviakov, Alexei F.
other author:	Zhao, Peng.
Published:	Cham :Springer International Publishing :2024.
Description:	xviii, 309 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Differential equations, Nonlinear.
Online resource:	https://doi.org/10.1007/978-3-031-53074-6
ISBN:	9783031530746$q(electronic bk.)

Analytical properties of nonlinear partial differential equationswith applications to shallow water models /
Cheviakov, Alexei F.

Analytical properties of nonlinear partial differential equationswith applications to shallow water models /[electronic resource] :Alexei Cheviakov, Peng Zhao. - Cham :Springer International Publishing :2024. - xviii, 309 p. :ill. (some col.), digital ;24 cm. - CMS/CAIMS books in mathematics,v. 102730-6518 ;. - CMS/CAIMS books in mathematics ;v. 3..

Equations of Fluid dynamics and the shallow water approximation -- Integrability and related analytical properties of nonlinear PDE systems -- Analytical properties of some classical shallow-water models -- Discussion.

Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence transformations, local and nonlocal symmetries, conservation laws, and more. Modern computational approaches and symbolic software can be employed to systematically derive and use such properties, and where possible, construct exact and approximate solutions of nonlinear equations. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs. Examples include both well known nonlinear PDEs and less famous systems that arise in the context of shallow water waves and far beyond. The book will be of interest to researchers and graduate students in applied mathematics, physics, and engineering, and can be used as a basis for research, study, reference, and applications.

ISBN: 9783031530746$q(electronic bk.)

Standard No.: 10.1007/978-3-031-53074-6doiSubjects--Topical Terms:

185178
Differential equations, Nonlinear.

LC Class. No.: QA372

Dewey Class. No.: 515.355

Analytical properties of nonlinear partial differential equationswith applications to shallow water models /
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520 $a Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence transformations, local and nonlocal symmetries, conservation laws, and more. Modern computational approaches and symbolic software can be employed to systematically derive and use such properties, and where possible, construct exact and approximate solutions of nonlinear equations. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs. Examples include both well known nonlinear PDEs and less famous systems that arise in the context of shallow water waves and far beyond. The book will be of interest to researchers and graduate students in applied mathematics, physics, and engineering, and can be used as a basis for research, study, reference, and applications.
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