Results 1 to 10 of about 86,829 (231)

Simple identification of fake Lax pairs

, 2013
Two simple ways to identify and explain fake Lax pairs are provided. The two methods are complementary, one involves finding a gauge transformation which can be used to remove the associated nonlinear system's dependent variable(s) from a fake Lax pair. The second method shows that excess degrees of freedom exist in fake Lax pairs.
Butler, Samuel, Hay, Mike
openaire   +2 more sources

1+1 spectral problems arising from the Manakov-Santini system

, 2010
This paper deals with the spectral problem of the Manakov Santini system. The point Lie symmetries of the Lax pair have been identified. Several similarity reductions arise from these symmetries. An important benefit of our procedure is that the study of
Bluman G W, Bogdanov L V, Chang J H Chen Y T, Estévez P G, Ibragimov N, J Prada, M L Gandarias, M S Bruzón, Olver P J, P G Estévez, Pavlov M V Chang J H Chen Y T, Stephani H   +11 more
core   +1 more source

Integrability, exact solutions and nonlinear dynamics of a nonisospectral integral-differential system

Open Physics, 2019
The investigations of integrability, exact solutions and dynamics of nonlinear partial differential equations (PDEs) are vital issues in nonlinear mathematical physics.
Xu Bo, Zhang Sheng
doaj   +1 more source

Finite dimensional Hamiltonian system related to Lax pair with symplectic and cyclic symmetries

, 2011
For the 1+1 dimensional Lax pair with a symplectic symmetry and cyclic symmetries, it is shown that there is a natural finite dimensional Hamiltonian system related to it by presenting a unified Lax matrix.
Zhou, Zi-Xiang
core   +1 more source

N=2 supersymmetric hyperbolic Calogero-Sutherland model

Nuclear Physics B, 2020
The N=2 supersymmetric hyperbolic Calogero-Sutherland model obtained in arXiv:1902.08023 by gauging the N=2 superfield matrix system is studied. Classical and quantum N=2 supersymmetry generators are found.
Sergey Fedoruk
doaj   +1 more source

Systematic derivation of boundary Lax pairs

, 2007
We systematically derive the Lax pair formulation for both discrete and continuum integrable classical theories with consistent boundary conditions.
Avan, Jean, Doikou, Anastasia
openaire   +2 more sources

Exact solutions of a local fractional nonisospectral complex mKdV equation based on Riemann–Hilbert method with time-varying spectrum

Alexandria Engineering Journal
This article combines the Riemann–Hilbert method with fractional power-law time-varying spectrum for the first time to solve a time fractional nonisospectral complex mKdV (tfniscmKdV) equation. Firstly, the tfniscmKdV equation and its associated Lax pair
Bo Xu, Sheng Zhang
doaj   +1 more source

Bäcklund Transformation and Quasi-Periodic Solutions for a Variable-Coefficient Integrable Equation

Abstract and Applied Analysis, 2014
Binary Bell polynomials are applied to construct bilinear formalism, bilinear Bäcklund transformation, Lax pair, and infinite conservation laws of the generalized variable-coefficient fifth-order Korteweg-de Vries equation.
Wenjuan Rui, Yufeng Zhang
doaj   +1 more source

Quantum Lax Pairs via Dunkl and Cherednik Operators [PDF]

Communications in Mathematical Physics, 2019
Minor editorial changes to the introduction.
openaire   +4 more sources

The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I

Symmetry, Integrability and Geometry: Methods and Applications, 2011
We wish to explore a link between the Lax integrability of the q-Painlevé equations and the symmetries of the q-Painlevé equations. We shall demonstrate that the connection preserving deformations that give rise to the q-Painlevé equations may be thought
Christopher M. Ormerod
doaj   +1 more source