On classification of integrable non-evolutionary equations
可精确求解与可积系统
2007-05-23 v1
摘要
We study partial differential equations of second order (in time) that possess a hierarchy of infinitely many higher symmetries. The famous Boussinesq equation is a member of this class after the extension of the differential polynomial ring. We develop the perturbative symmetry approach in symbolic representation. Applying it, we classify the integrable equations of 4th and 6th order (in the space derivative) equations, as well as we have found three new 10th order integrable equations. To prove the integrability we provide the corresponding bi-Hamiltonian structures and recursion operators.
引用
@article{arxiv.nlin/0601046,
title = {On classification of integrable non-evolutionary equations},
author = {Alexander V. Mikhailov and Vladimir S. Novikov and Jing Ping Wang},
journal= {arXiv preprint arXiv:nlin/0601046},
year = {2007}
}
备注
22 pages