Dynamic patterns of high-order rogue waves for Sasa-Satsuma equation. (English) Zbl 1345.35106
The paper aims to produce generalized higher-order rational and semi-rational solutions to the Sasa-Satsuma equation, which is an integrable extension of the nonlinear Schrödinger equation for a complex functions \(q(x,t)\):
\[
iq_t -q_{xx} - 2| q|^2q + i[6(| q|^2q)_x -3(| q|^2)_xq +q_{xxx}] = 0.
\]
By means of a modified dressing method, higher-order mixed rational-breather solutions are constructed via finding the respective Bloch (alias Jost) functions, in terms of the respective inverse scattering transform, and the related Schur polynomials. Under special conditions imposed on parameters, the mixed solutions go over into purely rational ones, which represent higher-order rogues waves.
Reviewer: Boris A. Malomed (Tel Aviv)
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 37K15 | Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems |
Keywords:
integrable NLS-type equations; dressing transformation; breathers; inverse scattering transform; Bloch functions; Schur polynomialReferences:
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