The expansions of spectral function and the corresponding finite dimensional integrable systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:477

Article

Du, Dianlou¹  Wang, Xue¹ 

[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China

关键词: Integrable system;    Action-angle coordinates;    Inversion;    Soliton solutions;   

DOI  :  10.1016/j.jmaa.2019.04.065

来源: Elsevier

【 摘 要 】

In this paper, taking the Lax pairs of KdV equation as an illustrative example, with the help of a transformation of the spectral problem, another form of spectral function is used to give finite dimensional integrable systems. These integrable systems are generated by two different kinds of polynomial expansion of spectral function on spectral parameter. Further, the root variables of the spectral function are introduced to study the canonical equations of Hamilton. Finally, based on the Hamilton-Jacobi theory, the action-angle variables are built and the soliton solutions of KdV equation are obtained by inversion. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free