000			04014cam a22003858i 4500
001			55390
005			20250619122235.0
008			221102s2023 flu b 001 0 eng
010			_a 2022052684
020			_a9781032429212 _q(hardback)
020			_a9781032441160 _q(paperback)
020			_z9781003370543 _q(ebook)
040			_aNU _beng _erda _cDLC
041			_aENG
042			_apcc
082	0	0	_a515 VUP 2023 _223/eng20230119
100	1		_aVu, Pham Loi, _eauthor.
245	1	0	_aInverse scattering problems and their application to nonlinear integrable equations / _cPham Loi Vu, Institute of Mechanics and the National Foundation for Science and Technology Development (NAFOSTED), Vietnam.
250			_aSecond edition.
263			_a2302
264		1	_aBoca Raton : _bCRC Press, _c2023.
300			_axxix,422 pages : _b illustrations ; _c24 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	0		_aMonographs & research notes in mathematics
500			_aRevised edition of: Inverse scattering problems and their application to nonlinear integrable equations / Pham Loi Vu. 1. 2019.
504			_aIncludes bibliographical references and index.
520			_a"Inverse Scattering Problems and Their Applications to Nonlinear Integrable Equations, Second Edition is devoted to inverse scattering problems (ISPs) for differential equations and their applications to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, differential equations, and equations of mathematical physics. This book is intended for a wide community working with ISPs and their applications. There is an especially strong traditional community in mathematical physics. In this monograph, the problems are presented step-by-step, and detailed proofs are given for considered problems to make the topics more accessible for students who are approaching them for the first time. New to the Second Edition All new chapter dealing with the Backlund transformations between a common solution of both linear equations in the Lax pair and the solution of the associated IBVP for NLEEs on the half-line Updated references and concluding remarks Features Solving the direct and ISP, then solving the associated initial value problem (IVP) or initial-boundary value problem (IBVP) for NLEEs are carried out step-by-step. The unknown boundary values are calculated with the help of the Lax (generalized) equations, then the time-dependent scattering data (SD) are expressed in terms of preassigned initial and boundary conditions. Thereby, the potential functions are recovered uniquely in terms of the given initial and calculated boundary conditions. The unique solvability of the ISP is proved and the SD of the scattering problem is described completely. The considered ISPs are well-solved. The ISPs are set up appropriately for constructing the Backhund transformations (BTs) for solutions of associated IBVPs or IVPs for NLEEs. The procedure for finding a BT for the IBVP for NLEEs on the half-line differs from the one used for obtaining a BT for non-linear differential equations defined in the whole space. The interrelations between the ISPs and the constructed BTs are established to become new powerful unified transformations (UTs) for solving IBVPs or IVPs for NLEEs, that can be used in different areas of physics and mechanics. The application of the UTs is consistent and efficiently embedded in the scheme of the associated ISP"-- _cProvided by publisher.
650		0	_aMathematics
776	0	8	_iOnline version: _aVu, Pham Loi. _tInverse scattering problems and their application to nonlinear integrable equations _bSecond edition. _dBoca Raton : C&H/CRC Press, 2023 _z9781003370543 _w(DLC) 2022052685
906			_a7 _bcbc _corignew _d1 _eecip _f20 _gy-gencatlg
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999			_c55390 _d55390