Envelope solitons, multi-peak solitons and breathers in optical fibers via Chupin Liu's theorem and polynomial law of nonlinearity

This paper studies the (1 + 1)-dimensional nonlinear Schrodinger equation via polynomial law of nonlinearity which arises in nonlinear optical fibers and Bragg gratings. The envelope solitons as a entire are separated into two types: dark and bright solitons, which exist in the anomalous and normal dispersion regions, respectively. Grey and black optical soli tons of the stated model are reported through appropriate complex envelope ansatz solution. With the usage of Chupin Liu's theorem to the grey and black solitons, we evaluate new categories of combined optical soliton solutions. In addition, propagation behaviours for homoclinic breathers, multiwaves and M-shaped rational solitons are analytically examined via logarithmic transformation with ansatz functions approach. Multiwave solitons are reported by using three-waves technique. Furthermore two kinds of interactions for M-shape soliton through exponential functions are examined.