Exploration traveling solitary solutions to the mKdV-Zakharov-Kuznetsov equation with advection noise

In this paper, we consider the stochastic modified Korteweg-de Vries-Zakharov-Kuznetsov (SmKdV-ZK) equation, which is driven in the Itô sense by advection noise. We show that by solving certain deterministic counterparts of the modified Korteweg-de Vries-Zakharov-Kuznetsov (for short DmKdV-ZK) with an extra diffusion term, and then merging the results with a solution of stochastic ordinary differential equations, the exact solution of the SmKdV-ZK equation may be discovered. We derive the soliton solutions for the DmKdV-ZK equation using two distinct methods: the extended tanh function method and the $\exp (-\Phi (\eta ))$-expansion method. Moreover, we show how the advection noise impacts the solutions of the SmKdV-ZK equation by presenting several 3D graphs using a MATLAB software.