Boundary-value problems on the half-plane for the Ishimori equation that are compatible with the inverse scattering method

1992 ◽  
Vol 91 (3) ◽  
pp. 581-590 ◽  
Author(s):  
I. T. Khabibullin
Keyword(s):  
Boundary Value Problems ◽  
Inverse Scattering ◽  
Half Plane ◽  
Boundary Value ◽  
Inverse Scattering Method ◽  
Scattering Method

EXPLICIT BÄCKLUND TRANSFORMATION OF BREATHER SOLUTION FOR THE SINE-GORDON EQUATION

1989 ◽  
Vol 04 (07) ◽  
pp. 667-673 ◽  
Author(s):  
YI XIAO ◽  
NIANNING HUANG
Keyword(s):  
Inverse Scattering ◽  
Half Plane ◽  
Soliton Solution ◽  
Gordon Equation ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Sine Gordon Equation ◽  
Breather Solution ◽  
Upper Half Plane ◽  
Explicit Expressions

Explicit expressions of the Bäcklund transformations generating a soliton solution and a breather solution for the sine-Gordon equation are given. Solutions are shown to be regular without the restriction of λj, in the upper half-plane of complex λ, which is given by the inverse scattering method.

scholarly journals Integrable extended Hubbard models with boundary Kondo impurities

2001 ◽  
Vol 64 (3) ◽  
pp. 445-467
Author(s):  
Anthony J. Bracken ◽  
Xiang-Yu Ge ◽  
Mark D. Gould ◽  
Huan-Qiang Zhou
Keyword(s):  
Hilbert Space ◽  
Bethe Ansatz ◽  
Inverse Scattering ◽  
Magnetic Moments ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Ansatz Method ◽  
One Dimensional ◽  
Hubbard Models ◽  
Kondo Impurities

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z2-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

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