Fractal Higher-order Dispersions Model and Its Fractal Variational Principle Arising in the Field of Physcial Process

This paper introduces the fractal version of the higher-order dispersion model for the construction of novel soliton solutions through fractal variational technology. Higher-order dispersion model theoretical study of the soliton propagation dynamics is known in the absence of self-phase modulation. In the context of negligibly small group velocity dispersion, this model involves higher-order spatio-temporal dispersion and can be a core component of the telecommunications industry. Using the variational approach, the model effectively produces bright and dark soliton solutions. Essential novel conditions guaranteeing the existence of suitable solitons have been developed. The 3D, 2D and contour graphs of the computed effects are seen in the collection of the relevant parameter values. This study shows the significance and immense latency of variational technologies to the derivative nonlinear Schrödinger equation (DNLSE).