The nonlinear optical transmission equation was investigated in the presence of detuning, inter-modal dispersion, time- and space-modulated external potentials, and dissipation. Optical solitons, triangular periodic solutions, and Jacobian elliptic periodic solutions are constructed with the aid of the self-similarity transformation and Jacobian elliptic equation expansion methods. The conditions for analytical solutions to exist are obtained. Both Kerr-law as well as parabolic-law nonlinear media are considered.
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Zhou et al. (2013) studied this question.
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