Strongly localized modes in binary discrete media with cubic-quintic nonlinearity : an anti-continuum approach - Lukhman bin Abdul Taib (Kulliyyah of Science, International Islamic University Malaysia, 2018)
This study is aim to investigate the existence and stability of strongly localized modes (SLMs) in binary discrete media with cubic-quintic nonlinearity described by two-component cubic-quintic discrete nonlinear Schrödinger equations (CQDNLSEs). The existence of the solutions are demonstrated by solving the steady state equations of the model, while their stability are shown by using the standard linearization ansatz. The space-time evolution of the solutions are executed by performing direct numerical integrations of the coupled CQDNLSEs. In the first part, we derive analytical expressions essential for the existence of bright SLMs. New family of SLMs are introduced too, namely the symbiotic even-odd bright modes. Stability analysis showed that quintic nonlinearity yields effect on the instability of odd anti-symmetric and shifted bright modes. Meanwhile for even bright SLMs, solutions that are in the bound state of odd modes or in the state of out-of-phase tend to become stable. In the second part, we perform the derivation of analytical expressions for dark modes. We found that stability of odd and even dark modes confirm the results on modulational stability region identified by Baizakov et al. (2009), but the symbiotic dark SLMs are not constrained by it. For odd and even dark modes, instability of the solutions give rise to localized states. The existence of symbiotic dark–anti-dark modes are restricted to a small range of parameters. For symbiotic bright-dark SLMs, modes with even structure are shown to be unstable compared to odd feature.