Modulation instability and nonlinear dynamics in the (2 + 1)-dimensional complex mKdV system: innovative soliton solutions via Jacobi elliptic function method

This paper explores the (2 + 1)-dimensional complex modified Korteweg–de Vries (cmKdV) system using the Jacobi elliptic function expansion method. The primary goal is to analyse modulation instability and derive innovative soliton solutions. We then solve the resulting equation using the Jacobi elliptic function expansion method, which is capable of producing a wide variety of solutions, including periodic, kink and bright soliton solutions. Figures show graphical representations of the found solutions in multiple-dimension computations using 2D, 3D and contour sketches. The findings indicate that the technique used are effective and reliable tools that can be used to solve a variety of nonlinear differential equations.