%0 Journal Article
%T INVERSE SCATTERING TRANSFORM AND REGULAR RIEMANN-HILBERT PROBLEM<br>反散射变换和正规Riemann-Hilbert问题
%A WANG SHI-KUN
%A GUO HAN-YING
%A WU KE
%A <br>王世坤
%A 郭汉英
%A 吴可
%J 物理学报
%D 1983
%I 
%X It is shown that the inverse scattering transform method to solve the Lax pair of given nonlinear evolution equation can be reduced to a kind of Riemann-Hilbert (R-H) problem of meromorphic functions with respect to the complex spectral parameter. The R-H problem is generally regular no matter whether the solitons are involved in it. The linear singular integral equation connected with the R-H problem has been derived, which is essencially equivalent to the Gel'fand-Levitan-Marchenko equation. Furthermore, the regular R-H problem satisfied by the Darboux-B?cklund transformation from a fundamental solution set of the eigenvalue equation of Lax pair to a new set has been given as well. The R-H problem reduced from the inverse scattering transform is in fact a special case of that satisfied by the Darboux-Backlund transformation.
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=47EA7CFDDEBB28E0&jid=29DF2CB55EF687E7EFA80DFD4B978260&aid=C9BA238B946A8760C01A8D60A0542DD6&yid=A7F20A391020FDEE&vid=9971A5E270697F23&iid=59906B3B2830C2C5&sid=87A9A510C01DA8C7&eid=15863C3A31AE2538&journal_id=1000-3290&journal_name=物理学报&referenced_num=0&reference_num=0