000			01630nam a2200181la 4500
005			20250808114651.0
008			250808s9999 xx 000 0 und d
020			_a9780582239630
082			_a515.352 _bILI
100			_aIliev, I D
245		0	_aSpectral Methods in Soliton Equations _cIliev, I D; Khristov, Eugeni; Kirchev, Kiril Petrov
260			_bCRC Press _c1994
300			_a412 pages
520			_aSoliton theory as a method for solving some classes of nonlinear evolution equations (soliton equations) is one of the most actively developing topics in mathematical physics. This book presents some spectral theory methods for the investigation of soliton equations ad the inverse scattering problems related to these equations. The authors give the theory of expansions for the Sturm-Liouville operator and the Dirac operator. On this basis, the spectral theory of recursion operators generating Korteweg-de Vries type equations is presented and the Ablowitz-Kaup-Newell-Segur scheme, through which the inverse scattering method could be understood as a Fourier-type transformation, is considered. Following these ideas, the authors investigate some of the questions related to inverse spectral problems, i.e. uniqueness theorems, construction of explicit solutions and approximative methods for solving inverse scattering problems. A rigorous investigation of the stability of soliton solutions including solitary waves for equations which do not allow integration within inverse scattering method is also presented.
650			_aMathematics
700	1		_aKhristov, Eugeni _aKirchev, Kiril Petrov
942			_cENGLISH
999			_c579324 _d579324