10.46298/ocnmp.9809
https://ocnmp.episciences.org/9809
Fokas, A. S.
A. S.
Fokas
Latifi, A.
A.
Latifi
The nonlinear Schr\"odinger equation with forcing involving products of eigenfunctions
We elaborate on a new methodology, which starting with an integrable
evolution equation in one spatial dimension, constructs an integrable forced
version of this equation. The forcing consists of terms involving quadratic
products of certain eigenfunctions of the associated Lax pair. Remarkably, some
of these forced equations arise in the modelling of important physical
phenomena. The initial value problem of these equations can be formulated as a
Riemann-Hilbert problem, where the "jump matrix" has explicit x and t
dependence and can be computed in terms of the initial data. Thus, these
equations can be solved as efficiently as the nonlinear integrable equations
from which they are generated. Details are given for the forced versions of the
nonlinear Schrodinger.
Comment: 20 pages, no figure, this paper is published in the journal Open
Communications in Nonlinear Mathematical Physics
episciences.org
Nonlinear Sciences - Exactly Solvable and Integrable Systems
37K10
2022-07-31
2022-08-02
2022-08-02
eng
journal article
arXiv:2207.07463
10.48550/arXiv.2207.07463
2802-9356
https://ocnmp.episciences.org/9809/pdf
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Open Communications in Nonlinear Mathematical Physics
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