| Abstract: |
| Kinks connecting zero and nonzero equilibria in the NLS equation with competing nonlinearities occur at the special values of the frequency parameter. Since they are minimizers of energy, they are expected to be orbitally stable in the time evolution of the NLS equation. However, the stability proof is complicated by the degeneracy of kinks near
the nonzero equilibrium. The main purpose of this work is to give a rigorous proof of the orbital stability of kinks. We give details of analysis and computations for the cubic-quintic NLS equation and show how the proof is extended to the general case. We also identify the orbitally stable solitons in the discrete version of this model and perform a comprehensive numerical study of all stable configurations in the anti-continuum limit of the model. |
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