Abstract
We consider the generalized nonlinear Schrödinger equation describing the propagation of ultrashort pulses in nonlinear metamaterials and find exact combined solitary wave solutions describing the simultaneous propagation of bright and dark solitary waves in a combined form. Based on the Drude model, we discuss the existence conditions and the properties of the combined solitary waves. Furthermore, we analytically and numerically investigate the stability of the combined solitary waves under small perturbations. The results show that bright and dark solitary waves may combine together under certain conditions and propagate stably with a proper form in metamaterials.
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