A generalized isospectral–nonisospectral heat equation hierarchy and its expanding integrable model

A generalized nonisospectral heat integrable hierarchy with three dependent variables is singled out. A Bäcklund transformation of a resulting isospectral integrable hierarchy is produced by converting the usual Lax pair into the Lax pairs in Riccati forms. In addition, an expanding integrable model...

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Bibliographic Details
Published inAdvances in difference equations Vol. 2020; no. 1; pp. 1 - 24
Main Authors Lu, Huanhuan, Zhang, Yufeng, Mei, Jianqin
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 05.09.2020
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Bäcklund transformation
Conserved density
Dependent variables
Difference and Functional Equations
Functional Analysis
Mathematics
Mathematics and Statistics
Nonisospectral integrable hierarchy
Ordinary Differential Equations
Partial Differential Equations
Thermodynamics
Nonisospectral integrable hierarchy
Conserved density
Bäcklund transformation
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Summary:A generalized nonisospectral heat integrable hierarchy with three dependent variables is singled out. A Bäcklund transformation of a resulting isospectral integrable hierarchy is produced by converting the usual Lax pair into the Lax pairs in Riccati forms. In addition, an expanding integrable model is also worked out by making use of a set of linear spectral problems which are introduced via a high-dimensional loop algebra. Finally, we obtain some conserved densities of a types of heat integrable system by using the weight theory on PDEs.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-02930-4