A New Finite-dimensional Integrable System Associated to (1+1)-dimensional Soliton Equations

WEI Han-yu, GUO Han-dong, XIA Tie-cheng

doi:10.13371/j.cnki.chin.q.j.m.2015.04.003

Chinese Quarterly Journal of Mathematics >

2015 , Vol. 30 >Issue 4: 503 - 514

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.04.003

A New Finite-dimensional Integrable System Associated to (1+1)-dimensional Soliton Equations

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1. College of Mathematics and Statistics, Zhoukou Normal University 2. Department of Mathematics, Shanghai University 3. College of Arts and Sciences, Sias Iternational College of Zhengzhou University

WEI Han-yu(1982-), male, native of Zhoukou, Henan, a lecturer of Zhoukou Normal University, Ph.D., engages in solitons and integrable systems.

Received date: 2013-09-18

Online published: 2020-11-19

Supported by

Supported by the National Natural Science Foundation of China(11271008;61072147;11447220)； Supported by the First-class Discipline of Universities in Shanghai； Supported by the Science and Technology Department of Henan Province(152300410230)；

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Abstract

In this paper, a new spectral problem is proposed and the corresponding soliton equations hierarchy are also obtained. Under a constraint between the potentials and the eigenfunctions, the eigenvalue problem is nonlinearized so as to be a new finitedimensional Hamiltonian system. By resotring to the generating function approach, we obtain conserved integrals and the involutivity of the conserved integrals. The finite-dimensional Hamiltonian system is further proved to be completely integrable in the Liouville sense. Finally, we show the decomposition of the soliton equations.

Key words： nonlinearization; Bargmann constraint; Hamiltonian system; conserved integral

Cite this article

WEI Han-yu, GUO Han-dong, XIA Tie-cheng . A New Finite-dimensional Integrable System Associated to (1+1)-dimensional Soliton Equations[J]. Chinese Quarterly Journal of Mathematics, 2015 , 30(4) : 503 -514 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.04.003

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