# American Institute of Mathematical Sciences

October  2011, 4(5): 1019-1031. doi: 10.3934/dcdss.2011.4.1019

## Variational approximations of bifurcations of asymmetric solitons in cubic-quintic nonlinear Schrödinger lattices

 1 Fakultät für Mathematik, Universität Karlsruhe, Karlsruhe 76128, Germany 2 Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1

Received  April 2009 Revised  September 2009 Published  December 2010

Using a variational approximation we study discrete solitons of a nonlinear Schrödinger lattice with a cubic-quintic nonlinearity. Using an ansatz with six parameters we are able to approximate bifurcations of asymmetric solutions connecting site-centered and bond-centered solutions and resulting in the exchange of their stability. We show that the numerical and variational approximations are quite close for solitons of small powers.
Citation: Christopher Chong, Dmitry Pelinovsky. Variational approximations of bifurcations of asymmetric solitons in cubic-quintic nonlinear Schrödinger lattices. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1019-1031. doi: 10.3934/dcdss.2011.4.1019
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