Maximum error estimates for a compact difference scheme of the coupled nonlinear Schrödinger–Boussinesq equations

The coupled nonlinear Schrodinger-Boussinesq (SBq) equations describe the nonlinear development of modulational instabilities associated with Langmuir field amplitude coupled to intense electromagnetic wave in dispersive media such as plasmas. In this paper, we present a conservative compact difference scheme for the coupled SBq equations and analyze the conservative property and the existence of the scheme. Then we prove that the scheme is convergent with convergence order O(tau(2) + h(4)) in L-infinity-norm and is stable in L-infinity-norm. Numerical results verify the theoretical analysis.