A Scheme for Generating Nonisospectral Integrable Hierarchies and Its Related Applications

• 作者: Yu Feng ZHANG Xiang Zhi ZHANG
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（5）
• 页码范围: 707-730
• 页数: 24页
• 语种: 英文

摘要

Under the framework of the complex column-vector loop algebra Cp, we propose a scheme for generating nonisospectral integrable hierarchies of evolution equations which generalizes the appli-cable scope of the Tu scheme. As applications of the scheme, we work out a nonisospectral integrable Schr?dinger hierarchy and its expanding integrable model. The latter can be reduced to some non-isospectral generalized integrable Schr?dinger systems, including the derivative nonlinear Schr?dinger equation once obtained by Kaup and Newell. Specially, we obtain the famous Fokker–Plank equation and its generalized form, which has extensive applications in the stochastic dynamic systems. Finally, we investigate the Lie group symmetries, fundamental solutions and group-invariant solutions as well as the representation of the tensor of the Heisenberg group H3 and the matrix linear group SL(2, R) for the generalized Fokker–Plank equation (GFPE).