Please use this identifier to cite or link to this item:
http://dx.doi.org/10.25673/54776
Title: | Bifurcation of gap solitons in coupled mode equations in d dimensions |
Author(s): | Dohnal, Tomáš Wahlers, Lisa |
Issue Date: | 2021 |
Type: | Article |
Language: | English |
Abstract: | We consider a system of first order coupled mode equations in Rd describing the envelopes of wavepackets in nonlinear periodic media. Under the assumptions of a spectral gap and a generic assumption on the dispersion relation at the spectral edge, we prove the bifurcation of standing gap solitons of the coupled mode equations from the zero solution. The proof is based on a Lyapunov–Schmidt decomposition in Fourier variables and a nested Banach fixed point argument. The reduced bifurcation equation is a perturbed stationary nonlinear Schrödinger equation. The existence of solitary waves follows in a symmetric subspace thanks to a spectral stability result. A numerical example of gap solitons in R2 is provided. |
URI: | https://opendata.uni-halle.de//handle/1981185920/56728 http://dx.doi.org/10.25673/54776 |
Open Access: | Open access publication |
License: | (CC BY 4.0) Creative Commons Attribution 4.0 |
Sponsor/Funder: | Publikationsfonds MLU |
Journal Title: | Journal of dynamics and differential equations |
Publisher: | Springer Science + Business Media B.V. |
Publisher Place: | New York, NY [u.a.] |
Original Publication: | 10.1007/s10884-021-09971-7 |
Appears in Collections: | Open Access Publikationen der MLU |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Dohnal-Wahlers2021_Article_BifurcationOfGapSolitonsInCoup.pdf | 952.26 kB | Adobe PDF | View/Open |