No abstract

In this paper, we consider the fractional ion sound and Langmuir waves (FISALWs) equation. We apply the unified solver technique in order to extract some new solutions for the FISALWs equation. The fractional derivative is defined in the sense of a conformable fractional derivative. The proposed solver is based on He’s semi-inverse method and gives beneficial solutions in explicit form. The recital of the method is trustworthy and useful and gives new, more general exact solutions. The constraint conditions for the existence of valid soliton solutions are reported. The enforcement of the presented solutions might be especially interesting in the applications of plasma physics such as bursty waves in cusp regions, Langmuir turbulence, and solar wind. Finally, the proposed solver can be extended to many other models in new physics and applied science.

The nonlinear Schrödinger’s equations (NLSEs) is a famous model used to investigate the propagation of optical solitons via nonlinear optical fibers. We applied the unified solver method in order to extract some new stochastic solutions for three types of NLSEs forced by multiplicative noise in Itô sense. The acquired solutions describe the propagation of solitons in nonlinear optical fibers. We exhibit the influence of presence of noise term on the solution for the NLSEs. The theoretical analysis and presented solutions illustrate that the proposed solver is powerful and efficient. Finally, the wave amplitudes may be controlled by the effects performance of physical parameters of the NLSEs in the presence of noise term in Itô sense. Finally, we present He’s frequency formulation.

No abstract