New Complex hyperbolic function solutions for the (2+1)-Dimensional dispersive long water-wave system

Abstract

In this paper, new algorithms called the "Modified exp(-?)-expansion function method" and "Improved Bernoulli sub-equation function method" have been proposed. The first algorithm is based on the exp(-?(?))-expansion method; the latter is based on the Bernoulli sub-Ordinary Differential Equation method. The methods proposed have been expressed comprehensively in this manuscript. The analytical solutions and application results are presented by drawing the two- And three-dimensional surfaces of solutions such as hyperbolic, complex, trigonometric and exponential solutions for the (2+1)-dimensional dispersive long water-wave system. Finally, a conclusion has been presented by mentioning the important discoveries in this manuscript.