Therefore our method is a pure algebraic algorithm which can be applied to integrable system
and non-integrable system
MOSER, Finitely many mass points on the line under the influence of an exponential potential--an integrable system
, in Dynamical Systems.
A completely integrable system
(or simply an integrable system
) on a 2n-dimensional symplectic manifold (M, [omega]) is a smooth map F := ([f.
An integrable system
on a symplectic manifold (M, [omega]) of dimension 2N is a set of N functions which are functionally independent and mutually Poisson-commutative.
Furthermore, it also gives an essential tool for the study of a tropical integrable system
known as the box-ball system (see e.
relation which can be understood as a completely integrable system
of PDEs (of the second order) with the unknown function x(t), too.
which can be understood as a completely integrable system
of PDE (of the second order) with the unknown function x(t), too.
It was shown in  that the integrable system
is deformed as well.
Based on the new approach to such systems, Which i suggested recently, I aim to prove certain conjectures about the structure of hierarchies of topological type, Describe them explicitly in important examples and also find connections to other areas in the theory of integrable systems
Using this framework of integrable systems
, Wheeler-Zinn-Justin  recently obtained another equivariant Littlewood-Richardson rule for factorial Grothendieck polynomials.
Through their employment in combinatorics on one hand and connection to the Yang-Baxter equation on the other, Rota-Baxter algebras found their way into mathematical physics, in particular the renormalisation of quantum field theories  and, most recently, integrable systems
The first two nonlinear integrable systems
in hierarchy (26) are as follows: