Wave phenomena in a wavelength-specific reflector for the Kundu–Mukherjee–Naskar system in optics and photonics

In this research, the coupled variation of the (2+1)-dimensional Kundu–Mukherjee–Naskar (KMN) equation, which governs the wave dynamics in fiber Bragg grating (FBG), is analyzed. This version models the interaction between two nonlinear waves, while the single mode of this equation characterizes nonlinear wave propagation in a single channel or medium where only one wave is considered. To find analytical solutions, the new version trial equation method (NVTEM) is regarded due to its wide range of solution structures. Analytic wave solutions are not just mathematical constructs but also help reveal the underlying physical mechanisms. Motivated by this, the present work derives and analyzes a variety of exact wave solutions to the coupled KMN equation, such as rogue-like soliton, double-peaked bound state, high-order rogue waves, and bright-lump solution supported by symbolic computation to ensure their validity. The KMN system is first converted to a nonlinear ordinary differential equation (NLODE) via the complex wave transform. Applying the proposed technique, rational, exponential, hyperbolic, and Jacobi elliptic type solutions have been acquired. The two and three-dimensional plots have been utilized to depict the dynamics of our constructed findings and to establish the abundance of the proposed analytical technique as well. Besides, some physical implications may be mentioned through interesting aspects in our findings.