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
|0(OCoLC)fst00978098
650 7 Nonlinear integral equations.|2fast|0(OCoLC)fst01038791
830 0 Monographs and research notes in mathematics