Multistable Solitons in the Cubic-Quintic Discrete Nonlinear Schr'odinger Equation

摘要

We analyze the existence and stability of localized solutions in theone-dimensional discrete nonlinear Schr\"{o}dinger (DNLS) equation with acombination of competing self-focusing cubic and defocusing quintic onsitenonlinearities. We produce a stability diagram for different families ofsoliton solutions, that suggests the (co)existence of infinitely many branchesof stable localized solutions. Bifurcations which occur with the increase ofthe coupling constant are studied in a numerical form. A variationalapproximation is developed for accurate prediction of the most fundamental andnext-order solitons together with their bifurcations. Salient properties of themodel, which distinguish it from the well-known cubic DNLS equation, are theexistence of two different types of symmetric solitons and stable asymmetricsoliton solutions that are found in narrow regions of the parameter space. Theasymmetric solutions appear from and disappear back into the symmetric ones vialoops of forward and backward pitchfork bifurcations.