episciences.org_9809_1665087242
1665087242
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Open Communications in Nonlinear Mathematical Physics
28029356
10.46298/journals/ocnmp
https://ocnmp.episciences.org
08
02
2022
Volume 2
The nonlinear Schr\"odinger equation with forcing involving products of eigenfunctions
A. S.
Fokas
A.
Latifi
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
RiemannHilbert 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.
08
02
2022
9809
arXiv:2207.07463
10.48550/arXiv.2207.07463
https://arxiv.org/abs/2207.07463v2
10.46298/ocnmp.9809
https://ocnmp.episciences.org/9809

https://ocnmp.episciences.org/9884/pdf