Quantum Super-Integrable Systems as Exactly Solvable Models [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
Allan P Fordy
exaly +13 more sources
On differential equations invariant under two-variable M\"obius transformations [PDF]
Open Communications in Nonlinear Mathematical Physics, 2022 We compute invariants for the two-variable M\"obius transformation. In particular we are interested in partial differential equations in two dependent and two independent variables that are kept invariant under this transformation.
M. Euler, N. Euler, MC Nucci
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The solutions of classical and nonlocal nonlinear Schr\"{o}dinger equations with nonzero backgrounds: Bilinearisation and reduction approach [PDF]
Open Communications in Nonlinear Mathematical Physics, 2023 In this paper we develop a bilinearisation-reduction approach to derive solutions to the classical and nonlocal nonlinear Schr\"{o}dinger (NLS) equations with nonzero backgrounds.
Da-jun Zhang, Shi-min Liu, Xiao Deng
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Search for integrable two-component versions of the lattice equations in the ABS-list [PDF]
Open Communications in Nonlinear Mathematical Physics, 2022 We search and classify two-component versions of the quad equations in the ABS list, under certain assumptions. The independent variables will be called $y,z$ and in addition to multilinearity and irreducibility the equation pair is required to have the ...
Jarmo Hietarinta
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On fully-nonlinear symmetry-integrable equations with rational functions in their highest derivative: Recursion operators [PDF]
Open Communications in Nonlinear Mathematical Physics, 2022 We report a class of symmetry-intergable third-order evolution equations in 1+1 dimensions under the condition that the equations admit a second-order recursion operator that contains an adjoint symmetry (integrating factor) of order six.
Marianna Euler, Norbert Euler
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The nonlinear Schr\"odinger equation with forcing involving products of eigenfunctions [PDF]
Open Communications in Nonlinear Mathematical Physics, 2022 We elaborate on a new methodology, which starting with an integrable evolution equation in one spatial dimension, constructs an integrable forced version of this equation.
A. S. Fokas, A. Latifi
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Integrable Ito equations and properties of the associated Fokker-Planck equations [PDF]
Open Communications in Nonlinear Mathematical Physics, 2023 In a recent paper we have classified scalar Ito equations which admits a standard symmetry; these are also directly integrable by the Kozlov substitution.
Giuseppe Gaeta, Miguel Angel Rodriguez
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On Hamiltonian Formalism for Dressing Chain Equations of Even Periodicity [PDF]
Open Communications in Nonlinear Mathematical Physics, 2022 We propose a Hamiltonian formalism for $N$ periodic dressing chain with the even number $N$. The formalism is based on Dirac reduction applied to the $N+1$ periodic dressing chain with the odd number $N+1$ for which the Hamiltonian formalism is well ...
H. Aratyn, J. F. Gomes, A. H. Zimerman
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Derivation of Painlev\'e type system with $D_4^{(1)}$ affine Weyl group symmetry in a self-similarity limit [PDF]
Open Communications in Nonlinear Mathematical Physics, 2023 We show how the zero-curvature equations based on a loop algebra of $D_4$ with a principal gradation reduce via self-similarity limit to a polynomial Hamiltonian system of coupled Painlev\'e III models with four canonical variables and $D_4^{(1)}$ affine
H. Aratyn +3 more
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THE MARSDEN–WEINSTEIN REDUCTION STRUCTURE OF INTEGRABLE DYNAMICAL SYSTEMS AND A GENERALIZED EXACTLY SOLVABLE QUANTUM SUPERRADIANCE MODEL [PDF]
International Journal of Modern Physics B, 2013 An approach to describing nonlinear Lax type integrable dynamical systems of modern mathematical and theoretical physics, based on the Marsden–Weinstein reduction method on canonically symplectic manifolds with group symmetry, is proposed. Its natural relationship with the well-known Adler–Kostant–Souriau–Berezin–Kirillov method and the associated R ...
N. N. Bogolubov jr. +1 more
openaire +3 more sources