Elliptic solitons and “freak waves”. (English. Russian original) Zbl 1497.37080
St. Petersbg. Math. J. 33, No. 3, 523-551 (2022); translation from Algebra Anal. 33, No. 3, 129-168 (2021).
Summary: It is shown that elliptic solutions to the AKNS hierarchy equations can be obtained by exploring spectral curves that correspond to elliptic solutions of the KdV hierarchy. This also allows one to get the quasirational and trigonometric solutions for AKNS hierarchy equations as a limit case of the elliptic solutions mentioned above.
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |
| 35C08 | Soliton solutions |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35Q51 | Soliton equations |
Keywords:
KdV equation; NLS equation; AKNS hierarchy; finite-gap solution; spectral curve; theta functionReferences:
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