Results 91 to 100 of about 1,858,479 (279)

Deformed Harry Dym and Hunter-Zheng Equations

, 2003
We study the deformed Harry Dym and Hunter-Zheng equations with two arbitrary deformation parameters. These reduce to various other known models in appropriate limits.
Alber M. S., Ashok Das, Brunelli J. C., Brunelli J. C., Brunelli J. C., Faddeev L. D., Hereman W., Hunter J. K., J. C. Brunelli, Kadanoff L. P., Popowicz Z., Sabatier P. C., Sabatier P. C., Yi-Shen L., Ziemowit Popowicz   +14 more
core   +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

An Inverse Scattering Transform for the Lattice Potential KdV Equation

, 2011
The lattice potential Korteweg-de Vries equation (LKdV) is a partial difference equation in two independent variables, which possesses many properties that are analogous to those of the celebrated Korteweg-de Vries equation.
Ablowitz M J, Adler V E, Boiti M, Case K M, Case K M, Levi D, Mickens R E, Nalini Joshi, Nijhoff F, Samuel Butler, Shabat A   +10 more
core   +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

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

Darboux transformations for a Bogoyavlenskii equation in 2+1 dimensions

, 1999
We use the singular manifold method to obtain the Lax pair, Darboux transformations and soliton solutions for a (2+1) dimensional integrable equation.Comment: 7 pages, latex, to appear in the proceedings of the meeting "Nonlinearity and Integrability" (
Estevez, P. G., Hernaez, G. A.
core   +1 more source

Lax Pairs for the Modified KdV Equation

Axioms, 2023
Multi-parameter families of Lax pairs for the modified Korteweg-de Vries (mKdV) equation are defined by applying a direct method developed in the present study. The gauge transformations, converting the defined Lax pairs to some simpler forms, are found. The direct method and its possible applications to other types of evolution equations are discussed.
openaire   +2 more sources

ANALYSIS OF NONLINEAR EQUATIONS IN PRIVATE DERIVATIVES ASSOCIATED WITH THE THIRD-ORDER SCATTERING OPERATOR

Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020
Background. A plurality of nonlinear equations in partial derivatives having a Lax pair are either exactly integrable or equations that allow rich classes of exact solutions.
T. V. Red'kina, O. V. Novikova
doaj   +1 more source