The global attractor and numerical simulation of a forced weakly damped MKdV equation

In the paper long-time behavior of solutions derived from the dissipative MKdV equation in the unbounded domain is studied. The Sobolev interpolation inequality and prior estimate on time tt are applied to show the existence of solution in unbounded domain. Moreover, operator decomposition techniques and Kuratowskii αα-noncompacted measures are applied to study the smooth property of the solution. Existence of global attractor for dissipative MKdV equation in H2(R1)H2(R1) is proved. Then, the computational stability of universal double-time differential format is proved by using nature analysis approach and dissipative conservative scheme theory. Finally, accordant conclusion with theoretical proof is drawn by numerical simulation.