Abstract
We consider a generalized fourth-order nonlinear Schrödinger (NLS) equation. Based on the ansatz method, its bright, dark single-soliton is constructed under some constraint conditions. Furthermore, combining the Riccati equation extension approach, we also derive some exact singular solutions. With several parameters to play with, we display the dynamic behaviors of bright, dark single-soliton. Finally, the condition for the modulational instability (MI) of continuous wave solutions for the equation is generated. It is hoped that our results can help enrich the nonlinear dynamics of the NLS equations.
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