Results 31 to 40 of about 2,696,066 (112)

Darboux Integrability of Trapezoidal $H^{4}$ and $H^{6}$ Families of Lattice Equations II: General Solutions

, 2018
In this paper we construct the general solutions of two families of quad-equations, namely the trapezoidal $H^{4}$ equations and the $H^{6}$ equations.
Gubbiotti, Giorgio, Scimiterna, Christian, Yamilov, Ravil I.   +2 more
core   +1 more source

On the One Class of Hyperbolic Systems [PDF]

, 2006
The classification problem is solved for some type of nonlinear lattices. These lattices are closely related to the lattices of Ruijsenaars-Toda type and define the Backlund auto-transformations for the class of two-component hyperbolic systems.Comment ...
Adler, Vsevolod E., Shabat, Alexey B.
core   +4 more sources

$A_{n-1}$ Gaudin model with open boundaries

, 2005
The $A_{n-1}$ Gaudin model with integerable boundaries specified by non-diagonal K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method.
Abad, Amico, Babelon, Babujian, Bazhanov, Cambiaggio, Cao, Cherednik, de Vega, de Vega, Di Lorenzo, Dukelsky, Dukelsky, Feigin, Ghoshal, Gould, Hasegawa, Hikami, Hikami, Jimbo, Lima-Santos, Lima-Santos, Malara, Mezincescue, Nepomechie, Nepomechie, Perk, Ryu Sasaki, Schultz, Seiberg, Sklyanin, Sklyanin, von Delft, Wen-Li Yang, Yang, Yang, Yang, Yang, Yang, Yang, Yao-Zhong Zhang   +40 more
core   +1 more source

Coordinate Bethe Ansatz for Spin s XXX Model [PDF]

, 2011
We compute the eigenfunctions and eigenvalues of the periodic integrable spin s XXX model using the coordinate Bethe ansatz. To do so, we compute explicitly the Hamiltonian of the model.
Alonzi, Ludovic, Crampé, Nicolas, Ragoucy, Eric   +2 more
core   +5 more sources

Exact solution of the spin-isospin proton-neutron pairing Hamiltonian [PDF]

, 2007
The exact solution of proton-neutron isoscalar-isovector (T=0,1) pairing Hamiltonian with non-degenerate single-particle orbits and equal pairing strengths (g_{T=1}= g_{T=0}) is presented for the first time.
A. G. Ushveridze, B. Errea, Gaudin, J. Dukelsky, S. Lerma H., W. Satuła   +5 more
core   +2 more sources

Commuting Flows and Conservation Laws for Noncommutative Lax Hierarchies

, 2003
We discuss commuting flows and conservation laws for Lax hierarchies on noncommutative spaces in the framework of the Sato theory. On commutative spaces, the Sato theory has revealed essential aspects of the integrability for wide class of soliton ...
Boussinesq J., Date E., Gelfand I. M., Kadomtsev B. B., Masashi Hamanaka, Miwa T., Segal G.   +6 more
core   +1 more source

On a Quantization of the Classical $\theta$-Functions [PDF]

, 2015
The Jacobi theta-functions admit a definition through the autonomous differential equations (dynamical system); not only through the famous Fourier theta-series. We study this system in the framework of Hamiltonian dynamics and find corresponding Poisson
Brezhnev, Yurii V.
core   +4 more sources

On a two-parameter extension of the lattice KdV system associated with an elliptic curve

, 2002
A general structure is developed from which a system of integrable partial difference equations is derived generalising the lattice KdV equation. The construction is based on an infinite matrix scheme with as key ingredient a (formal) elliptic Cauchy ...
Adler V E, Adler V E, Bordag L A, Calogero F, Capel H W, Hirota R, Krichever I M, Nakamura A, Nakamura A, Nijhoff F W, Nijhoff F W, Nijhoff F W, Nijhoff F W, Nijhoff F W, Okamoto K, Papageorgiou V G, Quispel G R W, Quispel G R W, Svinolupov S I   +18 more
core   +2 more sources

Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones [PDF]

, 2007
There exists a large class of quantum many-body systems of Calogero-Sutherland type where all particles can have different masses and coupling constants and which nevertheless are such that one can construct a complete (in a certain sense) set of exact ...
Langmann, Edwin
core   +5 more sources

Three Dimensional Integrable Mappings [PDF]

, 2003
We derive three-dimensional integrable mappings which have two invariants.
arxiv   +1 more source