Solution of stochastic Allen–Cahn equation in the framework of soliton theoretical approach
Muhammad Sajid Iqbal, Aly R. Seadawy, Muhammad Zafarullah Baber, Muhammad Waqas Yasin, Nauman Ahmed
Abstract
In this paper, the Allen–Cahn equation with time noise is under consideration. The extended fan-sub technique is used to find the exact solutions. The solutions are successfully extracted in the form of hyperbolic, trigonometric and mixed forms of solitons. Importantly, the physical unique value problems of the solutions are discussed using the different values of parameters. The 2D, 3D, and their corresponding contour behaviors of these solutions are depicted by choosing the different values of parameters. The stability is controlled through the Borel coefficient in the noise term.
Topics & Concepts
Noise (video)TrigonometrySolitonTerm (time)Stability (learning theory)Mathematical analysisApplied mathematicsHyperbolic functionStatistical physicsMathematicsPhysicsComputer scienceNonlinear systemQuantum mechanicsMachine learningArtificial intelligenceImage (mathematics)Solidification and crystal growth phenomenaFluid Dynamics and Thin FilmsNonlinear Waves and Solitons