Numerical Stability Analysis of a Coupled Optical–Terahertz Schrödinger–Boussinesq Model with Quadratic Nonlinearity

Abstract

We examine a coupled optical--terahertz model of Schrödinger--Boussinesq type with quadratic nonlinearity and the numerical results reported in the source study. The continuous model combines a complex optical envelope equation with a real terahertz wave equation. We present its localized wave profile, normalization, centered finite-difference formulation, and two-stage optical iteration. We then distinguish that formal formulation from the explicit update routines used to generate the numerical figures. In the first experiment, the optical profile remains localized over early propagation layers; the terahertz field subsequently develops large excursions, followed by numerical blow-up in both fields. In a separate experiment, the plotted control factor multiplies fourth-order terahertz dispersion; the larger of two displayed factors produces stronger terahertz excursions. We formulate amplitude, residual, and grid-refinement diagnostics for assessing numerical instability and convergence. The available plots do not establish stability of the continuous soliton or a mesh-independent critical parameter.