Dressing the boundary: exact solutions of soliton equations on the half-line

Author(s):  
Cheng Zhang

Author(s):  
Ning Zhang ◽  
Tiecheng Xia

AbstractBy considering a new discrete isospectral eigenvalue problem, a hierarchy of integrable positive and negative lattice models is derived. It is shown that they correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. And the equation in the resulting hierarchy is integrable in Liouville sense. Further, a Darboux transformation is established for the typical equations by using gauge transformations of Lax pairs, from which the exact solutions are given.



2005 ◽  
Vol 46 (5) ◽  
pp. 052101 ◽  
Author(s):  
Martin Hallnäs ◽  
Edwin Langmann


2007 ◽  
Vol 21 (04) ◽  
pp. 189-197
Author(s):  
HAI-YONG DING ◽  
XI-XIANG XU ◽  
HONG-XIANG YANG ◽  
XIANG TIAN

A new isospectral problem is proposed and the corresponding integrable equation hierarchy is given. A Darboux transformation (DT) is derived to obtain the exact solutions for the typical lattice soliton equations.



1998 ◽  
Vol 09 (02) ◽  
pp. 265-269 ◽  
Author(s):  
W.-H. Steeb ◽  
Kiat Shi Tan ◽  
R. Stoop

We show how SymbolicC++, a symbolic and numeric computer algebra system written in C++, can be used to find exact solutions of soliton equations in (2+1)-dimensions.



Author(s):  
Fritz Gesztesy ◽  
Helge Holden ◽  
Johanna Michor ◽  
Gerald Teschl




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