Analytical Properties of Nonlinear Partial Differential Equations: with Applications to Shallow Water...

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Alexei Cheviakov Shanghai Maritime University

Analytical Properties of Nonlinear Partial Differential Equations

with Applications to Shallow Water Models

Alexei Cheviakov, Shanghai Maritime University

$278.95 $222.98

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English

Springer International Publishing AG
24 March 2024

Cybernetics & systems theory; Differential calculus & equations; Applied mathematics; Biology, life sciences

Series: CMS/CAIMS Books in Mathematics

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 beof 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.

By: Alexei Cheviakov, Shanghai Maritime University
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2024
Volume: 10
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9783031530739
ISBN 10: 303153073X
Series: CMS/CAIMS Books in Mathematics
Pages: 309
Publication Date: 24 March 2024
Audience: College/higher education , Further / Higher Education
Format: Hardback
Publisher's Status: Active

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.