We present a large set of exact analytic traveling-wavesolutions for the equation iut + uxx = a1u|u|2 + a2u|u|4 that can be of interest in higher-order nonlinear-optical media. This set includes all bright and dark solitary waves as well as periodic ones. Our procedure consists of direct integration; it is then purely algebraic and simple. Solutions are given in simple forms and tabulated.
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L. Gagnon (1989) studied this question.
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