Pseudospectral Renormalization Method for Solitons in Quasicrystal Lattice with the Cubic‐Quintic Nonlinearity

Nalan Antar

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

Abstract: We modified the spectral renormalization method as the pseudospectral renormalization method in order to find the localized solutions. The pseudospectral renormalization method can be applied to a large class of problems including different homogeneities. Using this computational method, we demonstrate the existence of two different solitons in optical media described by the self‐focusing cubic and the self‐defocusing quintic nonlinear Schrödinger equation with quasicrystal lattice. It is shown that there are two different lattice solitons corresponding to the first and the second renormalization factors for the self‐focusing cubic and the self‐defocusing quintic model. However, the self‐focusing quintic nonlinearity without optical lattice does not support two different solitons. We showed that the lattice solitons corresponding to the first and the second renormalization factors have the same powers and amplitudes. We also demonstrate that quintic nonlinearity supports bistable solitons by adding the optical lattice such as a quasicrystal lattice. The linear and nonlinear stabilities of these solitons are investigated using direct simulation of the nonlinear Schrödinger equation with the cubic‐quintic nonlinearity and its linearized equation.

Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2014/848153

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:848153

Access Statistics for this article

More articles in Journal of Applied Mathematics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().