Eur. Phys. J. D 59, 81-89 (2010)
https://doi.org/10.1140/epjd/e2010-00073-0

Solitons pinned to hot spots

¹ Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong
² Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, 69978, Israel

Corresponding author: ^a kwchow@hkusua.hku.hk

Received: 15 December 2009
Revised: 26 February 2010
Published online: 23 March 2010

Abstract

We generalize a recently proposed model based on the cubic complex Ginzburg-Landau (CGL) equation, which gives rise to stable dissipative solitons supported by localized gain applied at a “hot spot” (HS), in the presence of the linear loss in the bulk. We introduce a model with the Kerr nonlinearity concentrated at the HS, together with the local gain and, possibly, with the local nonlinear loss. The model, which may be implemented in laser cavities based on planar waveguides, gives rise to exact solutions for pinned dissipative solitons. In the case when the HS does not include the localized nonlinear loss, numerical tests demonstrate that these solitons are stable/unstable if the localized nonlinearity is self-defocusing/focusing. Another new setting considered in this work is a pair of two symmetric HSs. We find exact asymmetric solutions for it, although they are unstable. Numerical simulations demonstrate that stable modes supported by the HS pair tend to be symmetric. An unexpected conclusion is that the interaction between breathers pinned to two broad HSs, which are the only stable modes in isolation in that case, transforms them into a static symmetric mode.