Results 271 to 280 of about 4,590 (301)

Banach Algebras Associated to Lax Pairs

Reports on Mathematical Physics, 2015
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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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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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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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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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Covariance of Lax Pairs and Integrability of the Compatibility Condition

Theoretical and Mathematical Physics, 2001
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A Lax pair of the discrete Euler top

Journal of Physics A: Mathematical and Theoretical, 2017
Summary: We proposed the discrete Euler top in 2000 [\textit{R. Hirota} and the author, J. Phys. Soc. Japan 69, No. 3, 627--630 (2000; Zbl 1058.70504)]. In that paper, exact solutions and conserved quantities are described. However, a Lax pair of our proposed discrete Euler top is not contained. Moreover, the Lax pair is still unknown.
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A Primer on Lax Pairs

2020
L.M. Bates, R.C. Churchill
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