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Discrete Lax Pair for Discrete Toda Equation

Discrete Lax Pair for Discrete Toda Equation
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Lax pairs

Boletim da Sociedade Brasileira de Matemática, 1984
In the pioneering paper [Commun. Pure Appl. Math. 21, 467-490 (1968; Zbl 0162.411)], \textit{P. Lax} stated a condition under which certain one parameter families of operators \(\{\) L(t)\(\}\) are isospectral, i.e., all the L(t) have the same spectrum.
Neto, Hermano Frid, Thayer, F. Javier
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Lax pairs galore

Journal of Mathematical Physics, 1991
A formula that yields an (apparently—but only apparently—nontrivial) Lax pair for any nonlinear evolution PDE in 1+1 dimensions possessing a local conservation law is presented. Several examples are exhibited.
CALOGERO F., NUCCI, Maria Clara
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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
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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.
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Banach Algebras Associated to Lax Pairs

Reports on Mathematical Physics, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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.
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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.
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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
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