MARC 主機 00000cam  2200373Ii 4500 
001    1104907182 
003    OCoLC 
005    20200601213018.0 
008    190620s2020    flu      b    001 0 eng d 
020    0367334895 
020    9780367334895 
035    (OCoLC)1104907182 
040    YDX|beng|erda|cYDX|dYDXIT|dAS|dMATH 
050  4 QA371|b.P53 2020 
082 04 515.35|223 
100 1  Pham, Loi Vu,|eauthor 
245 10 Inverse scattering problems and their application to 
       nonlinear integrable equations /|cPham Loi Vu 
264  1 Boca Raton, FL :|bCRC Press,|c[2020] 
300    xxvi, 388 pages ;|c25 cm 
336    text|btxt|2rdacontent 
337    unmediated|bn|2rdamedia 
338    volume|bnc|2rdacarrier 
490 1  Monographs and research notes in mathematics 
504    Includes bibliographical references and index 
520    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 
650  0 Inverse problems (Differential equations) 
650  0 Nonlinear integral equations 
650  0 Scattering (Mathematics) 
650  7 Inverse problems (Differential equations)|2fast
650  7 Nonlinear integral equations.|2fast|0(OCoLC)fst01038791 
830  0 Monographs and research notes in mathematics 
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