In this paper,we propose a compact scheme to numerically study the coupled stochastic nonlinear Schrodinger equations.We prove that the compact scheme preserves the discrete stochastic multi-symplectic conservation law,discrete charge conservation law and discrete energy evolution law almost surely.Numerical experiments confirm well the theoretical analysis results.Furthermore,we present a detailed numerical investigation of the optical phenomena based on the compact scheme.By numerical experiments for various amplitudes of noise,we find that the noise accelerates the oscillation of the soliton and leads to the decay of the solution amplitudes with respect to time.In particular,if the noise is relatively strong,the soliton will be totally destroyed.Meanwhile,we observe that the phase shift is sensibly modified by the noise.Moreover,the numerical results present inelastic interaction which is different from the deterministic case.
In this paper,we develop a lattice Boltzmann model for a class ofone-dimensional nonlinear wave equations,including the second-order hyperbolictelegraph equation,the nonlinear Klein-Gordon equation,the damped and undampedsine-Gordon equation and double sine-Gordon equation.By choosing properly theconservation condition between the macroscopic quantity u,and the distributionfunctions and applying the Chapman-Enskog expansion,the governing equation isrecovered correctly from the lattice Boltzmann equation.Moreover,the local equilib-rium distribution function is obtained.The results of numerical examples have beencompared with the analytical solutions to confirm the good accuracy and the applica-bility of our scheme.
