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| Content Provider | Springer Nature Link |
|---|---|
| Author | Geng, Xianguo He, Guoliang Wu, Lihua |
| Copyright Year | 2013 |
| Abstract | Based on solving the Lenard recursion equations and the zero-curvature equation, we derive the Kaup–Kupershmidt hierarchy associated with a 3×3 matrix spectral problem. Resorting to the characteristic polynomial of the Lax matrix for the Kaup–Kupershmidt hierarchy, we introduce a trigonal curve $\mathcal {K}_{m-1}$ and present the corresponding Baker–Akhiezer function and meromorphic function on it. The Abel map is introduced to straighten out the Kaup–Kupershmidt flows. With the aid of the properties of the Baker–Akhiezer function and the meromorphic function and their asymptotic expansions, we arrive at their explicit Riemann theta function representations. The Riemann–Jacobi inversion problem is achieved by comparing the asymptotic expansion of the Baker–Akhiezer function and its Riemann theta function representation, from which quasi-periodic solutions of the entire Kaup–Kupershmidt hierarchy are obtained in terms of the Riemann theta functions. |
| Ending Page | 555 |
| Page Count | 29 |
| Starting Page | 527 |
| File Format | |
| ISSN | 09388974 |
| e-ISSN | 14321467 |
| Journal | Journal of Nonlinear Science |
| Issue Number | 4 |
| Volume Number | 23 |
| Language | English |
| Publisher | Springer-Verlag |
| Publisher Date | 2013-01-09 |
| Publisher Place | New York |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Relations with algebraic geometry, complex analysis, special functions ApplicationMathematics/Computational Methods of Engineering Trigonal curve Kaup–Kupershmidt hierarchy Quasi-periodic solutions Soliton theory, asymptotic behavior of solutions Analysis Theoretical, Mathematical and Computational Physics Theta functions; Schottky problem Mechanics Economic Theory |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Engineering Modeling and Simulation |
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