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We find the exact analytic form for solitary waves for arbitrary $k$ and find that they are a generalization of the exact solutions for the nonlinear Schr\\\"odinger equation (NLSE) and reduce to these solutions in a well defined nonrelativistic limit. 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We find the exact analytic form for solitary waves for arbitrary $k$ and find that they are a generalization of the exact solutions for the nonlinear Schr\\\"odinger equation (NLSE) and reduce to these solutions in a well defined nonrelativistic limit. 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