Soliton solutions of the nonlinear Schrodinger equation with the dual power law nonlinearity and resonant nonlinear Schrodinger equation and their modulation instability analysis

In optical fibers, the higher order nonlinear Schrodinger equations describe propagation of ultra-short pluse. The proposed modified simple equation method is employed to the nonlinear higher order Schrodinger equations for soliton solutions. The balance numbers in these Schrodinger equations are positive non-integers. The obtain solitary solutions are also presented by graphically. The modulation instability analysis shows the stability and movement of the waves, which confirms that all obtained solutions are analytical and stable. This is a new and standardized method which is applicable to solve different kind of problems in mathematics and physics. (C) 2017 Elsevier GmbH. All rights reserved.