Optical solitons for Kudryashov's model: undetermined coefficients with Jacobi's elliptic functions

This paper recovers solitons solutions with Kudryashov's proposed law of refractive index having quadruple power-law of nonlinear refractive index. The method of undetermined coefficients is the integration algorithm where the starting hypotheses are Jacobi's elliptic functions. A full spectrum of soliton solutions are recovered when the modulus of ellipticity approaches unity.