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作者 Pham, Loi Vu, author
書名 Inverse scattering problems and their application to nonlinear integrable equations / Pham Loi Vu
出版項 Boca Raton, FL : CRC Press, [2020]
國際標準書號 0367334895
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QA371 .P53 2020    在架上    30340200566515
說明 xxvi, 388 pages ; 25 cm
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
系列 Monographs and research notes in mathematics
Monographs and research notes in mathematics
附註 Includes bibliographical references and index
Inverse 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
主題 Inverse problems (Differential equations)
Nonlinear integral equations
Scattering (Mathematics)
Inverse problems (Differential equations) fast (OCoLC)fst00978098
Nonlinear integral equations. fast (OCoLC)fst01038791
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