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Online ISSN 1552-4485; Print ISSN 0033-569X
Localization in optical systems with an intensity-dependent dispersion
Authors:
R. M. Ross, P. G. Kevrekidis and D. E. Pelinovsky
Journal:
Quart. Appl. Math. 79 (2021), 641-665
MSC (2020):
Primary 35Q55, 35Q60, 35P15
DOI:
https://doi.org/10.1090/qam/1596
Published electronically:
May 27, 2021
MathSciNet review:
4328142
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We address the nonlinear Schrödinger equation with intensity-dependent dispersion which was recently proposed in the context of nonlinear optical systems. Contrary to the previous findings, we prove that no solitary wave solutions exist if the sign of the intensity-dependent dispersion coincides with the sign of the constant dispersion, whereas a continuous family of such solutions exists in the case of the opposite signs. The family includes two particular solutions, namely cusped and bell-shaped solitons, where the former represents the lowest energy state in the family and the latter is a limit of solitary waves in a regularized system. We further analyze the delicate analytical properties of these solitary waves such as their asymptotic behavior near singularities, the convergence of the fixed-point iterations near such solutions, and their spectral stability. The analytical theory is corroborated by means of numerical approximations.
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Additional Information
R. M. Ross
Affiliation:
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515
MR Author ID:
1318638
Email:
rmross@umass.edu
P. G. Kevrekidis
Affiliation:
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515
MR Author ID:
657357
ORCID:
0000-0002-7714-3689
Email:
kevrekid@math.umass.edu
D. E. Pelinovsky
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada; and Department of Applied Mathematics, Nizhny Novgorod State Technical University, Nizhny Novgorod, 603950, Russia
MR Author ID:
355614
ORCID:
0000-0001-5812-440X
Email:
dmpeli@math.mcmaster.ca
Received by editor(s):
March 22, 2021
Received by editor(s) in revised form:
April 2, 2021
Published electronically:
May 27, 2021
Additional Notes:
The third author acknowledges financial support from the state task program in the sphere of scientific activity of the Ministry of Science and Higher Education of the Russian Federation (Task No. FSWE-2020-0007) and from the grant of the president of the Russian Federation for the leading scientific schools (grant No. NSH-2485.2020.5). This material is based upon work supported by the US National Science Foundation under Grant DMS-1809074 (PGK)
Article copyright:
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Brown University