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

2021 ◽  
pp. 456-476
Author(s):  
Cheng Zhang
Keyword(s):  
Exact Solutions ◽  
Half Line ◽  
Soliton Equations

A Hierarchy of Lattice Soliton Equations Associated with a New Discrete Eigenvalue Problem and Darboux Transformations

2015 ◽  
Vol 16 (7-8) ◽  
pp. 301-306 ◽  
Author(s):  
Ning Zhang ◽  
Tiecheng Xia
Keyword(s):  
Eigenvalue Problem ◽  
Exact Solutions ◽  
Spectral Parameter ◽  
Darboux Transformation ◽  
Lattice Models ◽  
Darboux Transformations ◽  
Discrete Eigenvalue ◽  
Negative Power ◽  
Soliton Equations ◽  
Gauge Transformations

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.

scholarly journals Exact solutions of two complementary one-dimensional quantum many-body systems on the half-line

2005 ◽  
Vol 46 (5) ◽  
pp. 052101 ◽  
Author(s):  
Martin Hallnäs ◽  
Edwin Langmann
Keyword(s):  
Exact Solutions ◽  
Half Line ◽  
Many Body ◽  
One Dimensional ◽  
Many Body Systems

A NEW HIERARCHY OF DISCRETE INTEGRABLE MODEL AND ITS DARBOUX TRANSFORMATION

2007 ◽  
Vol 21 (04) ◽  
pp. 189-197
Author(s):  
HAI-YONG DING ◽  
XI-XIANG XU ◽  
HONG-XIANG YANG ◽  
XIANG TIAN
Keyword(s):  
Exact Solutions ◽  
Darboux Transformation ◽  
Integrable Model ◽  
Integrable Equation ◽  
Soliton Equations ◽  
Isospectral Problem

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.

Exact Solutions of (2+1)-Dimensional Soliton Equations Applying SymbolicC++

1998 ◽  
Vol 09 (02) ◽  
pp. 265-269 ◽  
Author(s):  
W.-H. Steeb ◽  
Kiat Shi Tan ◽  
R. Stoop
Keyword(s):  
Exact Solutions ◽  
Computer Algebra ◽  
Computer Algebra System ◽  
Soliton Equations ◽  
Dimensional Soliton

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.

Soliton Equations and their Algebro-Geometric Solutions

2008 ◽  
Author(s):  
Fritz Gesztesy ◽  
Helge Holden ◽  
Johanna Michor ◽  
Gerald Teschl
Keyword(s):  
Soliton Equations ◽  
Geometric Solutions

Exact solutions for simple spin clusters with isotropic Heisenberg exchange interactions

1993 ◽  
Vol 90 ◽  
pp. 1077-1100 ◽  
Author(s):  
E Belorizky ◽  
PH Fries
Keyword(s):  
Exact Solutions ◽  
Exchange Interactions ◽  
Heisenberg Exchange ◽  
Spin Clusters
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