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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| Published in | Journal of nonlinear science Vol. 35; no. 5 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.10.2025
Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 0938-8974 1432-1467 |
| DOI | 10.1007/s00332-025-10203-1 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 106 |
| Author | Tian, Shou-Fu Cao, Li-Ming |
| Author_xml | – sequence: 1 givenname: Li-Ming surname: Cao fullname: Cao, Li-Ming organization: School of Mathematics, China University of Mining and Technology – sequence: 2 givenname: Shou-Fu surname: Tian fullname: Tian, Shou-Fu email: sftian@cumt.edu.cn, shoufu2006@126.com organization: School of Mathematics, China University of Mining and Technology |
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| Cites_doi | 10.1016/S0370-1573(96)00049-X 10.1016/j.physd.2008.03.050 10.1111/sapm.12335 10.1111/j.1467-9590.2010.00496.x 10.1137/19M1240757 10.1111/sapm.12287 10.1175/1520-0469(1972)029<0680:FABWP>2.0.CO;2 10.1016/j.physleta.2010.08.007 10.1080/03091929608213634 10.3934/dcds.2009.25.1163 10.1016/j.physd.2017.08.010 10.1016/j.cnsns.2014.06.012 10.1016/j.geomphys.2015.03.010 10.1098/rspa.1979.0084 10.1002/cpa.21819 10.1002/cpa.3160270108 10.1016/j.cnsns.2016.11.014 10.1007/s11071-013-0998-1 10.1111/sapm.12166 10.1088/0305-4470/28/11/024 10.1007/s00332-021-09722-4 10.1016/j.physd.2017.01.004 10.1142/4513 10.1016/j.aim.2023.109356 10.1002/sapm1974534249 10.1093/imamat/13.3.367 10.1017/CBO9780511546723 10.1111/1467-9590.00401 10.1088/1751-8113/44/28/285201 10.1007/BF00913182 10.1016/j.physd.2010.03.005 10.1007/978-3-642-52803-3 10.1016/j.jcp.2006.03.020 |
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| Snippet | We investigate in the present work the spectral stability of elliptic function solutions for the AB system, a completely integrable model for the description... |
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| SubjectTerms | 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 |
| Title | Spectral Stability of Elliptic Solutions for the AB System |
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