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

Christopher Chong; Dmitry Pelinovsky

doi:10.3934/dcdss.2011.4.1019

Article Contents

2011, Volume 4, Issue 5: 1019-1031. Doi: 10.3934/dcdss.2011.4.1019

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

Christopher Chong^1, and
Dmitry Pelinovsky^2,

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

Received: March 31, 2009

Revised: August 31, 2009

Published: September 2011

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Abstract

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:

Discrete nonlinear Schrödinger equations,
Bifurcations of discrete solitons,
Variational approximations.

Mathematics Subject Classification: Primary: 35Q55, 37K60, 35B32; Secondary: 58E30.

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