On discrete stochastic p-Laplacian complex-valued Ginzburg-Landau equations driven by superlinear Lévy noise

Our work is focused on discrete stochastic p-Laplacian complex-valued Ginzburg-Landau equations influenced by superlinear Lévy noise, under the assumption that the drift and diffusion terms satisfy local Lipschitz continuity. We begin by demonstrating the existence and uniqueness of solutions, as well as the weak pullback mean random attractors of the system. Following this, we demonstrate the existence of invariant probability measures and explore their limit properties as the parameters $(a_1,\epsilon ,\hat{\epsilon })$ converge to $(a_{1,0},{\epsilon }_0,{\hat{\epsilon }}_0)\in [0,1]\times [0,1]\times [0,1]$. The main challenges addressed include handling the superlinear diffusion, nonlinear drift terms, and the nonlinear p-Laplacian operator, as well as establishing the tightness of the distribution law for the solution family and corresponding invariant probability measures. To find solutions to these challenges, we use the strategy of stopping times and uniform tail-end bounds. Finally, it should be noted that each limit of a sequence of invariant probability measures of discrete stochastic p-Laplacian Ginzburg-Landau model disturbed by superlinear Lévy noise ought to be a invariant probability measure of the discrete stochastic p-Laplacian Schrödinger model disturbed by superlinear Lévy noise.