HYBRID-TYPE MODEL AND THE DIRECT SUM OF QUANTUM GROUPS

1991 ◽  
Vol 06 (13) ◽  
pp. 1177-1183 ◽  
Author(s):  
TETSUO DEGUCHI ◽  
AKIRA FUJII
Keyword(s):  
Quantum Group ◽  
Inverse Scattering ◽  
Quantum Groups ◽  
Group Structure ◽  
Formal Group ◽  
Inverse Scattering Method ◽  
Type Model ◽  
Scattering Method ◽  
Direct Sum ◽  
Hybrid Type

We present the quantum formal group derived from the hybrid-type model. The quantum group structure is given by the direct sum of several quantum groups. We show that by applying the quantum inverse scattering method to the direct sum of the several quantum groups we can reconstruct the hybrid-type model.

Inverse scattering transform in two spatial dimensions for the N-wave interaction problem with a dispersive term

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mansur I. Ismailov
Keyword(s):  
Inverse Scattering ◽  
Wave Interaction ◽  
Inverse Scattering Method ◽  
Type Model ◽  
Time Interval ◽  
Scattering Method ◽  
Degenerate Kernel ◽  
Small Initial Data ◽  
Uniqueness Of The Solution ◽  
Interaction Problem

Abstract A dispersive N-wave interaction problem ( N = 2 ⁢ n {N=2n} ), involving n velocities in two spatial and one temporal dimensions, is introduced. Explicit solutions of the problem are provided by using the inverse scattering method. The model we propose is a generalization of both the N-wave interaction problem and the ( 2 + 1 ) {(2+1)} matrix Davey–Stewartson equation. The latter examines the Benney-type model of interactions between short and long waves. Referring to the two-dimensional Manakov system, an associated Gelfand–Levitan–Marchenko-type, or so-called inversion-like, equation is constructed. It is shown that the presence of the degenerate kernel reads explicit soliton-like solutions of the dispersive N-wave interaction problem. We also present a discussion on the uniqueness of the solution of the Cauchy problem on an arbitrary time interval for small initial data.

scholarly journals INTRODUCTION TO QUANTUM INTEGRABILITY

2010 ◽  
Vol 25 (17) ◽  
pp. 3307-3351 ◽  
Author(s):  
ANASTASIA DOIKOU ◽  
STEFANO EVANGELISTI ◽  
GIOVANNI FEVERATI ◽  
NIKOS KARAISKOS
Keyword(s):  
Boundary Conditions ◽  
Bethe Ansatz ◽  
Inverse Scattering ◽  
Quantum Groups ◽  
Braid Group ◽  
Short Review ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Quantum Integrability ◽  
Basic Concepts

In this paper, we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang–Baxter and boundary Yang–Baxter equations depending on the choice of boundary conditions. The relation between the aforementioned equations and the braid group is briefly discussed. A short review on quantum groups as well as the quantum inverse scattering method (algebraic Bethe ansatz) is also presented.

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.

An inverse scattering method in time-domain electromagnetics

1981 ◽  
Vol 59 (10) ◽  
pp. 1348-1353
Author(s):  
Sujeet K. Chaudhuri
Keyword(s):  
Inverse Scattering ◽  
Time Domain ◽  
Random Noise ◽  
Power Series Expansion ◽  
Inverse Scattering Method ◽  
Wave Number ◽  
Moment Condition ◽  
Scattering Method ◽  
Fourth Moment ◽  
Rayleigh Coefficient

An inverse scattering model, based on the time-domain concepts of electromagnetic theory is developed. Using the first five (zeroth to fourth) moment condition integrals, the Rayleigh coefficient and the next higher order nonzero coefficient of the power series expansion in k (wave number) of the object backscattering response are recovered. The Rayleigh coefficient and the other coefficient thus recovered are used (with the ellipsoidal assumption for the object shape) to determine the dimensions and orientation of the object.Some numerical results of the application of this coefficient recovery technique to conducting ellipsoidal scatterers are presented. The performance of the software system in the presence of normally distributed random noise is also studied.

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