Abstract
The fourth-order nonlinear Schrödinger equation with four power nonlinearities is considered. The equation studied is the generalization of some well-known models and allows us to evaluate the influence various processes of pulse propagation. The main property of this equation is not integrability because the Cauchy problem for it cannot be solved by the inverse scattering transform. However this equation has some analytical solutions. Optical and embedded solitons corresponding to the considered mathematical model are given. Conservation laws of the partial differential equation for propagation pulses are found. Conservative quantities for the bright and embedded optical solitons are calculated.
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