On transverse stability of discrete line solitons

PHYSICA D-NONLINEAR PHENOMENA

卷:255

Article

Pelinoysky, Dmitry E.^1,2  Yang, Jianke³ 

[1] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4K1, Canada

[2] Nizhnii Novgorod State Tech Univ, Dept Appl Math, Nizhnii Novgorod, Russia

[3] Univ Vermont, Dept Math & Stat, Burlington, VT 05401 USA

关键词: Discrete NLS equations;    Line solitons;    Transverse stability;   

DOI  :  10.1016/j.physd.2013.03.011

来源: Elsevier

【 摘 要 】

We obtain sharp criteria for transverse stability and instability of line solitons in the discrete nonlinear Schrodinger equations on one- and two-dimensional lattices near the anti-continuum limit. On a two-dimensional lattice, the fundamental line soliton is proved to be transversely stable (unstable) when it bifurcates from the X (Gamma) point of the dispersion surface. On a one-dimensional (stripe) lattice, the fundamental line soliton is proved to be transversely unstable for both signs of transverse dispersion. If this transverse dispersion has the opposite sign to the discrete dispersion, the instability is caused by a resonance between isolated eigenvalues of negative energy and the continuous spectrum of positive energy. These results are obtained for focusing nonlinearity, and the results for defocusing nonlinearity can be deduced from a staggering transformation. When the line soliton is transversely unstable, asymptotic expressions for unstable eigenvalues are also derived. These analytical results are compared with numerical results and good agreement is obtained. (c) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free