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Existence of solitary waves in nonlinear equations of Schrödinger type
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
Christopher Chong 1, and Dmitry Pelinovsky 2,
Fakultät für Mathematik, Universität Karlsruhe, Karlsruhe 76128, Germany
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.
Keywords: Variational approximations., Discrete nonlinear Schrödinger equations, Bifurcations of discrete solitons.
Mathematics Subject Classification: Primary: 35Q55, 37K60, 35B32; Secondary: 58E3.
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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Christopher Chong Dmitry Pelinovsky