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We predict the existence of gray (dark) solitary waves in negative-index materials on the basis of a derived higher-order nonlinear Schrödinger equation. The conditions for the formation of three cases of gray solitary waves and exact analytical expressions are presented. Furthermore, we investigate the properties of these gray solitary waves in negative-index materials. The results show that the higher-order linear and nonlinear effects play a crucial role for the formation and properties of the second and third cases of gray solitary waves.
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Li et al. (2010) studied this question.
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