Highly dispersive optical solitons and solitary wave solutions for the (2+1)-dimensional Mel'nikov equation in modeling interaction of long waves with short wave packets in two dimensions.

In this paper, the optical soliton and solitary wave solutions of the (2 + 1) -dimensional Mel'nikov equation are investigated using the Kudryashov R function technique. The Kudryashov R function approach has various features that significantly facilitate symbolic computing, particularly for highly dispersive nonlinear equations. In computations, this approach has the benefit of not requiring the use of a certain function form. This approach gives an algorithm that is straightforward, efficient, and simple for finding solitary wave solutions. In addition, this approach is very influential and reliable when it comes to discovering hyperbolic function solutions of nonlinear equations. Many new hyperbolic function solutions have been obtained from the governing equation by using this technique. In addition, numerous types of soliton solutions describing various structures of optical solitons are retrieved. Using this method, breather, W-shaped, bell shaped, and bright soliton solutions have been generated from the governing equation. From the obtained results, it can be asserted that the applied approach may be a useful tool for addressing more highly nonlinear problems in various fields. By choosing particular values for the relevant parameters, the dynamic features of some breather, W-shaped, bell shaped and bright soliton solutions to the (2 + 1) -dimensional Mel'nikov equation have been displayed in 3D, 2D and contour graphs. [ABSTRACT FROM AUTHOR]