الحلول الموجية لبعض معادلات شرودنجر الغير خطية العشوائية ذات الضوضاء البيضاء المضاعفة باستخدام حسبان آتو

Abstract

In this thesis, some modern mathematical methods is applied to construct many types of solitons and other exact wave solutions equation in mathematical physics which have multiplicative white noise via Itȏ calculus with the aid of a computer algebraic system (CAS). The mathematical methods are the (G'/G, 1/G )-expansion method and the new Jacobi elliptic function expansion method for solving the nonlinear Biswas–Milovic equation (BME). The modified Kudryashov's-method and the addendum Kudryashov-method for solving the stochastic resonant nonlinear Schrodinger equation (stochastic resonant nonlinear-SE). The addendum Kudryashov-method for solving the nonlinear stochastic Radhakrishnan-Kundu Lakshmanan equation (RKL). Finally, a direct method based on the generalized Lienard equation is used for finding many other exact solutions of the stochastic resonant nonlinear-SE. Solitary wave solutions, hyperbolic functions solutions, periodic functions solutions, Jacobi elliptic functions solutions, rational functions solutions, dark soliton solutions, singular soliton solutions, bright soliton solutions are obtained. Based on reductive perturbation technique and a series of transformation, the nonlinear PDEs had been derived by many authors which can be reduced to a nonlinear ordinary differential equation (ODE) using the wave transformation. Furthermore, comparison between our new results and the well-known results is given. Finally, plotting 2D and 3D graphics of the exact solutions are shown.