Transformations and Instabilities of Higher-Order Solitons in Nonlinear Couplers and Their PT -Symmetric Counterparts

 

Rodislav Driben1,2 and Boris A. Malomed2

1Jerusalem College of Engineering, Ramat Beit HaKerem, POB 3566, Jerusalem, 91035, Israel

2 Department of Physical Electronics, School of Electrical Engineering,

Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel

 

Manuscript received May 15, 2012

Revised June 1, 2012

 

ABSTRACT

Dynamics of symmetric and antisymmetric 2-solitons and 3-solitons is studied in the model of the nonlinear dual-core coupler and its PT -symmetric version. Regions of the convergence of the injected perturbed symmetric and antisymmetric N-solitons into symmetric and asymmetric quasi- solitons are found. In the PT -symmetric system, with the balanced gain and loss acting in thetwo cores, borders of the stability against the blowup are identi¯ed. Notably, in all the cases thestability regions are larger for antisymmetric 2-soliton inputs than for their symmetric counterparts,

on the contrary to previously known results for fundamental solitons (N = 1). Dynamical regimes (switching) are also studied for the 2-soliton injected into a single core of the coupler. In particular, a region of splitting of the input into a pair of symmetric solitons is found, which is explained as a manifestation of the resonance between the vibrations of the 2-soliton and oscillations of energy between the two cores in the coupler.

 

 

Keywords : Dual-series equations, Fredholm integral equation, Hankel integral transform, Mixed boundary conditions, Partial differential equation, Rectangular plate, Singularities.

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