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040 _aOCoLC-P
_beng
_erda
_epn
_cOCoLC-P
020 _a9780429328459
_q(electronic bk.)
020 _a0429328451
_q(electronic bk.)
020 _a9781000709063
_q(electronic bk. : EPUB)
020 _a100070906X
_q(electronic bk. : EPUB)
020 _a9781000708684
_q(electronic bk. : PDF)
020 _a1000708683
_q(electronic bk. : PDF)
020 _z9780367334895
035 _a(OCoLC)1128095864
035 _a(OCoLC-P)1128095864
050 4 _aQA371
072 7 _aMAT
_x007000
_2bisacsh
072 7 _aMAT
_x007010
_2bisacsh
072 7 _aMAT
_x007020
_2bisacsh
072 7 _aPBKJ
_2bicssc
082 0 4 _a515.35
_223
100 1 _aPham, Loi Vu,
_eauthor.
245 1 0 _aInverse scattering problems and their application to nonlinear integrable equations /
_cPham Loi Vu.
250 _aFirst edition.
264 1 _aBoca Raton :
_bCRC Press,
_c2020.
300 _a1 online resource (xxvi, 388 pages).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aMonographs and research notes in mathematics.
505 0 _aChapter 1: Inverse scattering problems for systems of rst-order ODEs on a half-line Chapter 2: Some problems for a system of nonlinear evolution equations.on a half-line Chapter 3: Some problems for cubic nonlinear evolution equations on a half-line Chapter 4: The Dirichlet IBVPs for sine and sinh-Gordon equations Chapter 5: Inverse scattering for integration of the continual system of nonlinear interaction waves Chapter 6: Some problems for the KdV equation and associated inverse scattering Chapter 7: Inverse scattering and its application to the KdV equation with dominant surface tension Chapter 8: The inverse scattering problem for the perturbed string equation and its application to integration of the two-dimensional generalization from Korteweg-de Vries equation Chapter 9: Connections between the inverse scattering method and related methods
520 _aInverse Scattering Problems and Their Application to Nonlinear Integrable Equations is devoted to inverse scattering problems (ISPs) for differential equations and their application to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, partial differential equations, equations of mathematical physics, and functions of a complex variable. This book is intended for a wide community working with inverse scattering problems and their applications; in particular, there is a traditional community in mathematical physics. In this monograph, the problems are solved step-by-step, and detailed proofs are given for the problems to make the topics more accessible for students who are approaching them for the first time. Features " The unique solvability of ISPs are proved. The scattering data of the considered inverse scattering problems (ISPs) are described completely. " Solving the associated initial value problem or initial-boundary value problem for the nonlinear evolution equations (NLEEs) is carried out step-by-step. Namely, the NLEE can be written as the compatibility condition of two linear equations. The unknown boundary values are calculated with the help of the Lax (generalized) equation, and then the time-dependent scattering data (SD) are constructed from the initial and boundary conditions. " The potentials are recovered uniquely in terms of time-dependent SD, and the solution of the NLEEs is expressed uniquely in terms of the found solutions of the ISP. " Since the considered ISPs are solved well, then the SPs generated by two linear equations constitute the inverse scattering method (ISM). The application of the ISM to solving the NLEEs is consistent and is effectively embedded in the schema of the ISM.
588 _aOCLC-licensed vendor bibliographic record.
650 0 _aInverse problems (Differential equations)
650 0 _aNonlinear integral equations.
650 7 _aMATHEMATICS / Differential Equations
_2bisacsh
856 4 0 _3Taylor & Francis
_uhttps://www.taylorfrancis.com/books/9780429328459
856 4 2 _3OCLC metadata license agreement
_uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
999 _c126375
_d126375