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Solar radiation is a very useful form of energy such as heat and current density in gas turbines, nuclear power plants and thermal energy storage. The fundamental source of heat for multiple reactions in the climate, oceans, and ecological system is solar radiation. The current radiative flow model has significant applications in nuclear power generation, radioactive reactor cooling mechanisms, heating boilers, recycling of underground radioactive materials, fabrication of glass-fiber material and thermal textiles. The significance of study to reduce excessive heating by using magnetized surface. The main goal of current research is to report the Joule heating effect on heat and magnetic flux along the magnetic-driven porous cone under solar radiations and lower gravitational region. The novelty of this work is to explore wave oscillations in heat and magnetic flux with solar radiations under lower gravitational region. The Joule heating is applied to control the thermal boundary layer along gravity-driven cone. The coupled mathematical model is changed into non-dimensional form for physical parameters. The steady and oscillatory parts are obtained by using Stokes conditions. For smooth programming in FORTRAN computing tool, the primitive variables are used. The efficient finite difference scheme is used to plot the numerical findings with Gaussian elimination technique. The impact of governing parameters involved in the problem on wave oscillations of magnetic flux and heat transmission are drafted physically and numerically. It is noted that the fluid velocity enhances with significant amplitude as lower gravity and solar radiation increases along porous cone. It is found that wave oscillations of heat and magnetic flux increases as magnetic Prandtl number enhances under lower gravitational region.

The main objective of this paper is to retrieve the analytical solutions for a perturbed nonlinear Schrödinger’s equation. These achievements are obtained by following the basic steps of an efficient approach. The method we have used for the model is a completely novel and powerful technique that has not been used for the model so far. The basic common idea of the method is to convert the structure of the equation from a partial differential equation to an ordinary one using a new soliton wave variable. During the implementation of these methods, a variety of explicit solutions for different structures are extracted. For the sake of better understanding the dynamics of the solutions, several diagrams related to the introduced solutions are also plotted. We conclude that the employed method is an efficient tool for solving partial differential equations that paves the way to solve other practical models in the field. The software used in this article is Wolfram Mathematica.