Spectral Stability of Elliptic Solutions for the AB System

We investigate in the present work the spectral stability of elliptic function solutions for the AB system, a completely integrable model for the description of baroclinic waves in geophysical flow. With the aid of the algebraic geometry method, we derive the elliptic solutions of the AB system and...

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Bibliographic Details
Published inJournal of nonlinear science Vol. 35; no. 5
Main Authors Cao, Li-Ming, Tian, Shou-Fu
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2025
Springer Nature B.V
Subjects
Analysis
Baroclinic flow
Baroclinic waves
Classical Mechanics
Economic Theory/Quantitative Economics/Mathematical Methods
Eigenvectors
Elliptic functions
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Stability
Theoretical
Spectral stability
Subharmonic perturbations
37K45
Integrability
Elliptic function
35Q53
35Q51
AB system
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Summary:We investigate in the present work the spectral stability of elliptic function solutions for the AB system, a completely integrable model for the description of baroclinic waves in geophysical flow. With the aid of the algebraic geometry method, we derive the elliptic solutions of the AB system and its corresponding solutions of the Lax pair which are represented by theta functions. By establishing the squared-eigenfunction connection between the non-standard linear stability problem and the Lax spectral problem, we prove that the elliptic solutions are spectrally stable with respect to subharmonic perturbations.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0938-8974
1432-1467
DOI:10.1007/s00332-025-10203-1