Coupled higher-order nonlinear Schrödinger equations in nonlinear optics: Painlevé analysis and integrability

A set of coupled higher-order nonlinear Schr\"odinger equations which can be derived from the electromagnetic pulse propagations in coupled optical waveguides and in a weakly relativistic plasma with nonlinear coupling of two polarized transverse waves is proposed. Using the Painlev\'e singularity structure analysis, we show that it admits the Painlev\'e property and hence we expect that it will exhibit soliton-type lossless propagations.

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