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020 _a9783031530746
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024 7 _a10.1007/978-3-031-53074-6
_2doi
050 4 _aG70.23
072 7 _aPBW
_2bicssc
072 7 _aMAT003000
_2bisacsh
072 7 _aPBW
_2thema
110 2 _aShanghai Maritime University.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_973744
245 1 0 _aAnalytical Properties of Nonlinear Partial Differential Equations
_h[electronic resource] :
_bwith Applications to Shallow Water Models.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2024.
300 _aXVIII, 309 p. 18 illus., 5 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aCMS/CAIMS Books in Mathematics,
_x2730-6518 ;
_v10
505 0 _aEquations 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.
520 _aNonlinear 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.
650 0 _aGeography
_xMathematics.
_962343
650 0 _aMathematics.
_965523
650 0 _aDynamical systems.
650 0 _aBiomathematics.
_970325
650 1 4 _aMathematics of Planet Earth.
_973745
650 2 4 _aMathematics.
_965523
650 2 4 _aDynamical Systems.
650 2 4 _aMathematical and Computational Biology.
_970327
700 1 _aCheviakov, Alexei.
_eauthor.
_0(orcid)0000-0002-9647-3683
_1https://orcid.org/0000-0002-9647-3683
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_973746
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031530739
776 0 8 _iPrinted edition:
_z9783031530753
776 0 8 _iPrinted edition:
_z9783031530760
830 0 _aCMS/CAIMS Books in Mathematics,
_x2730-6518 ;
_v10
_971222
856 4 0 _uhttps://doi.org/10.1007/978-3-031-53074-6
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c58571
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