In this study, we investigate the optical soliton solutions, stability and sensitivity analysis of the (2+1)-dimensional complex modified Korteweg–de Vries (cmKdV) system of equations. To obtain soliton solutions, we utilized the newly developed extended auxiliary equation method, leading to a range of Jacobi elliptic function solutions. These solutions are further shown to reduce to bright, dark, singular, and periodic solitary wave solutions under specific parameter choices. In addition, a linear stability analysis is performed to derive the criterion for modulation instability (MI) associated with the continuous wave solutions of the considered equation. A detailed sensitivity analysis is also conducted under varying initial conditions to express that the equation is extremely sensitive. The physical behaviour of the obtained solutions is then visualized through the 3D graphical representations.
Thilagarajah Mathanaranjan (Thu,) studied this question.