Results 211 to 220 of about 1,858,479 (279)

Lax Pairs for Four-Wave Interaction Systems

Journal of the Physical Society of Japan, 1996
Summary: The Lax formulation for four-wave interaction systems is proposed. Integrable four-wave interaction models are derived from a compatibility condition between two linear equations. As simple examples, new four-wave interaction equations are explicitly given.
Tsuchida, Takayuki, Wadati, Miki
openaire   +1 more source

An extended (2+1)-dimensional modified Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff equation: Lax pair and Darboux transformation

Communications in Theoretical Physics
The aim of this paper is to study an extended modified Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff (mKdV-CBS) equation and present its Lax pair with a spectral parameter.
Li Cheng, Yi Zhang, Wen-Xiu Ma
semanticscholar   +1 more source

Lax Pair Equations and Connes-Kreimer Renormalization

Communications in Mathematical Physics, 2010
Lax pairs are often used to generate solutions to PDEs. Generally speaking, solutions of finite type to a given integrable PDE can be reduced to solving a system of ODEs or alternatively by finding a Birkhoff factorization. (For solutions of infinite type, more likely one must first solve a system of ODEs and then carry out a Birkhoff factorization ...
Baditoiu, G., Rosenberg, S.
openaire   +3 more sources

Banach Algebras Associated to Lax Pairs

Reports on Mathematical Physics, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Lax pair, binary Darboux transformations and dark-soliton interaction of a fifth-order defocusing nonlinear Schrödinger equation for the attosecond pulses in the optical fiber communication

Waves in Random and Complex Media, 2018
Under investigation in this paper is a fifth-order defocusing nonlinear Schrödinger equation for the attosecond pulses in the optical fiber communication.
Su‐Su Chen, B. Tian, Jun Chai, Xiao-Yu Wu, Zhong Du   +4 more
semanticscholar   +1 more source

Isospectral flow and lax pairs

Physics Letters A, 1984
Abstract Certain non-linear differential equations may be considered as compatibility conditions for a linear system of equations, that is, as the vanishing-curvature condition for some connection. It is shown how one can obtain this connection from an isospectral-flow condition using a Foldy-Wouthuysen transformation.
openaire   +1 more source

A Lax pair for Kowalevski's top

Physica D: Nonlinear Phenomena, 1987
We show that on each level surface of the invariants, the equations of the Kowalevski top are equivalent to a Neumann system describing the motion of a mass point on the sphere \(S^ 2:| p| =1\) under the influence of a force -Qp. This allows us to write a global Lax pair for the Kowalevski system and to show that Kowalevski's original reduction of the ...
Haine, L., Horozov, E.
openaire   +2 more sources

Lax-Pair-FIND: Discovering Lax pair from scarce data via deep learning

Chaos: An Interdisciplinary Journal of Nonlinear Science
With the flourishing development of data science and machine learning, significant progress has been made in solving forward and inverse problems of partial differential equations (PDEs) and discovering mathematical equations that describe physical systems.
Shuning Lin, Yong Chen
openaire   +1 more source

On the dispersionless Davey–Stewartson system: Hamiltonian vector field Lax pair and relevant nonlinear Riemann–Hilbert problem for dDS-II system

Letters in Mathematical Physics, 2018
In this paper, the semiclassical limit of Davey–Stewartson system is studied. It shows that the dispersionless limited integrable system of hydrodynamic type, which is defined as dDS (dispersionless Davey–Stewartson) system, arises from the commutation ...
G. Yi
semanticscholar   +1 more source

Two definitions of fake Lax pairs

AIP Conference Proceedings, 2015
Two definitions fake Lax pairs are provided. The two definitions 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 definition is related to excess degrees of freedom that exist in fake Lax pairs.
Samuel Butler, Mike Hay
openaire   +1 more source