LAUSR

In the paper, we are recovering optical solutions of the $$ (2 + 1)$$ -dimensional Schrodinger’s hyperbolic equation with nonlinearities of a higher order. It outlines the distribution of short-range pulses in optical fibers with nonlinear media. We develop new solutions of complex hyperbolic Schrodinger’s model using a method that is the latest extended direct algebraic method. This technique was combined with the fractional complex transformation of the optical solutions. Added various complex solutions trigonometric and hyperbolic are represented by single, dark, bright, and combined singular solution. The solutions that have been developed are more effective than the other techniques used. The extended algebraic method is a more efficient and robust mathematical technique arising from the propagation of optical pulse to produce new solitary optical wave solutions for several other nonlinear fractional-order equations. Plots 3D and 2D demonstrate solutions to describe the physical characteristics of that model. Also, the thorough study of two and three-dimensional optical solutions is explored together.