Algorithmic exact soliton families for a Stratonovich stochastic coupled Klein–Gordon–Schrödinger system with multiplicative amplitude noise

Purpose This study develops a computationally oriented framework to obtain exact coherent structures for a stochastic coupled Klein–Gordon–Schrödinger (KGS) system driven by multiplicative amplitude noise in the Stratonovich sense. Design/methodology/approach A traveling-wave reduction, combined with a mean-field representation of the stochastic exponential modulation, converts the stochastic PDE model into a deterministic nonlinear ODE system. Two algorithmic solvers are then implemented: the Enhanced Direct Algebraic Method and the New Projective Riccati Equation Method, which systematically generate closed-form solutions together with their parameter admissibility constraints. Findings The procedure yields families of bright, dark, kink-type, singular, straddled, and periodic waves expressed via hyperbolic and elliptic functions. Explicit parameter regimes are derived to guarantee real-valuedness and boundedness, and to quantify how free parameters control amplitude, width, and propagation speed under noise modulation. Originality/value The paper contributes reproducible solution algorithms and a benchmark catalogue of exact waveforms for validating numerical solvers and computer-aided engineering workflows involving stochastic coupled-wave dynamics in nonlinear dispersive media.