Lax equations, factorization and Riemann–Hilbert problems
Copyright policy )Lax equations, factorization and Riemann–Hilbert problems
The paper deals with the problem of existence and calculation of solutions to Lax equations that define finite-dimensional integrable systems. The method presented in the paper is based on Wiener–Hopf factorization and related Riemann–Hilbert problems on Riemann surfaces. The idea behind the method was first proposed by Semenov–Tian–Shansky but, to the authors' knowledge, is here applied, for the first time, in an infinite dimensional setting. The method dealt with in the paper enables one to analyse the global existence of solutions which seems more difficult by other methods. An example of a dynamical system associated with an elliptic curve is completely worked out in the paper.
- Instituto Superior de Espinho Portugal
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), infinite-dimensional setting, Global Riemannian geometry, including pinching, Riemann surfaces, finite-dimensional integrable systems, Riemann-Hilbert problems in context of PDEs, Wiener-Hopf factorization, Relationships between algebraic curves and integrable systems, Entire and meromorphic solutions to ordinary differential equations in the complex domain
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), infinite-dimensional setting, Global Riemannian geometry, including pinching, Riemann surfaces, finite-dimensional integrable systems, Riemann-Hilbert problems in context of PDEs, Wiener-Hopf factorization, Relationships between algebraic curves and integrable systems, Entire and meromorphic solutions to ordinary differential equations in the complex domain
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