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The primary goal of this paper is to seek solutions to the coupled nonlinear partial differential equations (CNPDEs) by the use of q-homotopy analysis transform method (q-HATM). The CNPDEs considered are the coupled nonlinear Schrödinger–Korteweg–de Vries (CNLS-KdV) and the coupled nonlinear Maccari (CNLM) systems. As a basis for explaining the interactive wave propagation of electromagnetic waves in plasma physics, Langmuir waves and dust-acoustic waves, the CNLS-KdV model has emerged as a model for defining various types of wave phenomena in mathematical physics, and so forth. The CNLM model is a nonlinear system that explains the dynamics of isolated waves, restricted in a small part of space, in several fields like nonlinear optics, hydrodynamic and plasma physics. We construct the solutions (bright soliton) of these models through q-HATM and present the numerical simulation in form of plots and tables. The solutions obtained by the suggested approach are provided in a refined converging series. The outcomes confirm that the proposed solutions procedure is highly methodological, accurate and easy to study CNPDEs. [ABSTRACT FROM AUTHOR]