Results 131 to 140 of about 3,408 (164)

Banach Algebras Associated to Lax Pairs

Reports on Mathematical Physics, 2015
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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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Generalized Lax pairs for the computation of semi-invariants

49th IEEE Conference on Decision and Control (CDC), 2010
A Lax pair is a classical tool for the computation of first integrals of continuous-time nonlinear systems. Semi-invariants extend the concept of first integral and generalize the concept of the pair (eigenvalue, left eigenvector) of a linear mapping to the nonlinear framework, whence play the role of basic bricks for the computation of Lyapunov ...
MENINI, LAURA, TORNAMBE', ANTONIO
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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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Separability and Lax pairs for Hénon–Heiles system

Journal of Mathematical Physics, 1993
The Hamiltonian system corresponding to the (generalized) Hénon–Heiles Hamiltonian H= 1/2(px2+py2)+1/2Ax2+1/2By2+x2y+εy3 is known to be integrable in the following three cases: (A=B, ε=1/3); (ε=2); (B=16A, ε=16/3). In the first two the system has been integrated by making use of genus one and genus two theta functions.
Ravoson, V., Gavrilov, L., Caboz, R.
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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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Discrete Lax pair for discrete Toda equation

Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 2003
Consider the Toda equation \[ \begin{aligned} & \tfrac1\delta(q_{n-1}(t+\delta)-q_{n-1}(t))=q_{n-1}(t+\delta)r_{n-1}(t+\delta)-q_{n-1}(t)r_n(t),\\ & \tfrac1\delta(r_n(t+\delta) - r_n(t))= q_{n-1}(t+\delta)-q_n(t)\end{aligned ...
Kyuya, Masuda, Masanobu, Murakata
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Constraint of discrete Lax equations with some special types of Lax pairs

2011 International Conference on Multimedia Technology, 2011
In this paper, firstly we deduce the constraint of discrete Lax equations with some special forms of Lax pairs. Then to illustrate the validity of the method, we construct two discrete Lax equations and successfully obtain their constraints by the method.
null Nianhua Li, Biao Li, null Hongmin Li, Yuqi Li   +3 more
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Covariance of Lax Pairs and Integrability of the Compatibility Condition

Theoretical and Mathematical Physics, 2001
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