03666nam a22005775i 4500 978-3-031-53074-6 DE-He213 20251030111738.0 cr nn 008mamaa 240322s2024 sz | s |||| 0|eng d 9783031530746 978-3-031-53074-6 10.1007/978-3-031-53074-6 doi G70.23 PBW bicssc MAT003000 bisacsh PBW thema Shanghai Maritime University. author. aut http://id.loc.gov/vocabulary/relators/aut 73744 Analytical Properties of Nonlinear Partial Differential Equations [electronic resource] : with Applications to Shallow Water Models. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XVIII, 309 p. 18 illus., 5 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda CMS/CAIMS Books in Mathematics, 2730-6518 ; 10 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. Geography Mathematics. 62343 Mathematics. 65523 Dynamical systems. Biomathematics. 70325 Mathematics of Planet Earth. 73745 Mathematics. 65523 Dynamical Systems. Mathematical and Computational Biology. 70327 Cheviakov, Alexei. author. (orcid)0000-0002-9647-3683 https://orcid.org/0000-0002-9647-3683 aut http://id.loc.gov/vocabulary/relators/aut 73746 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031530739 Printed edition: 9783031530753 Printed edition: 9783031530760 CMS/CAIMS Books in Mathematics, 2730-6518 ; 10 71222 https://doi.org/10.1007/978-3-031-53074-6 ZDB-2-SMA ZDB-2-SXMS 58571 58571