Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Open Communications in Nonlinear Mathematical Physics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.