The impact of standard Wiener process on the qualitative analysis and traveling wave solutions of stochastic nonlinear Kodama equation in the Stratonovich sense
Jin Wang, Li Zhao
Abstract
This article investigates the qualitative analysis and traveling wave solutions of the stochastic nonlinear Kodama equation within the Stratonovich framework. By applying a random traveling wave transformation, the equation is first converted into an ordinary differential equation. The qualitative behavior of the corresponding two-dimensional dynamical system and its perturbation is then examined using planar dynamical system analysis. Subsequently, the complete discriminant system method is employed to derive four distinct types of optical solutions. Three-dimensional plots illustrating these solutions under different parameters are also presented.
Topics & Concepts
Traveling waveMathematicsNonlinear systemQualitative analysisMathematical analysisDynamical systems theoryPerturbation (astronomy)PlanarOrdinary differential equationWiener processDynamical system (definition)Stochastic differential equationStochastic processApplied mathematicsDifferential equationHamiltonian systemPartial differential equationPerturbation theory (quantum mechanics)Sense (electronics)Statistical physicsWave equationNumerical analysisClassical mechanicsNonlinear Waves and SolitonsNonlinear Photonic SystemsQuantum chaos and dynamical systems