Energy balance approach to an optical solitons of (2+1)-dimensional fourth-order Korteweg–de Vries equation with two contemporary integration norms using a new mapping method

This work addresses the analytical solution of the fourth-Order Korteweg–de Vries (KdV4) equation, a nonlinear model describing the dynamics of optical soliton in (2+1) dimensions. To obtain exact results, we use the energy balance approach with two contemporary integration norms. The urgent need for precise mathematical representations in nonlinear optics, which are essential for developing optical communication and photonics, is addressed by this study. Complex optical soliton interactions are described by the (2+1)-dimensional KdV4 equation, which is essential to comprehending nonlinear light-matter interactions. The application of existing techniques is limited because they frequently ignore higher-order nonlinear effects. New exact solutions that capture higher-order nonlinear dynamics for optical solitons. computer simulations to confirm the accuracy and stability of the result. insights into the stability, propagation, and interactions of soliton. This study illustrates the effectiveness of the energy balance method in resolving nonlinear optical equations. Better design and optimisation of photonic devices are made possible by the obtained solutions, which offer a greater understanding of optical soliton behaviour. Modern integration rules are applied for the first time to the (2+1)-dimensional KdV4 problem. Higher-order nonlinear optics using the energy balance technique is extended. improved comprehension of optical soliton dynamics, going beyond what has been written so far. This work opens the door to more sophisticated mathematical modelling in nonlinear optics, which will support advancements in photonics, soliton-based computers, and optical communication. The energy balance approach is crucial in various fields such as physics, engineering, and interdisciplinary applications. It is used in optical communication systems, nonlinear optics, fiber optics, plasma physics, and Bose–Einstein condensates. It is also used in optical switching, amplifiers, interconnects, photonic devices, and quantum computing. The approach is also applied in mathematical and computational physics, where it is used to solve nonlinear PDEs, model complex physical systems, and study nonlinear phenomena. It is also used in biophotonics, materials science, chemical physics, environmental science, and biomedical engineering. Jacobi’s elliptic functions, solitons, are revealed by these schemes. They fall into one of four categories: bright, singular kink, and periodic solitons, are all included in the solutions that were produced. Two and three-dimensional simulations are then used to visualise the findings.