Unveiling single soliton solutions for the (3+1)-dimensional negative order KdV–CBS equation in a long wave propagation

Abstract

In this work, we investigate a fascinating negative-order Korteweg-de Vries Calogero-Bogoyavlenskii-Schiff equation in (3+1) dimensions, which is a collection of the Korteweg-de Vries equation and the Calogero-Bogoyavlenskii-Schiff equation. It has been looked that how this model defines the interactions of long wave propagations and how it may be used in math, physics, and engineering. We have used the unified method and the singular manifold method to determine the exact traveling wave solutions to this problem. Exponential, trigonometric, rational, and hyperbolic functions are used to represent the derived traveling wave solutions. By using the traveling wave transformation, the considered nonlinear partial differential equation is transformed into an ordinary differential equation. The full derivation of the provided model using the unified methodology and singular manifold method has been added. We have supposed that the equation has a soliton solution. We have got a system of equations by arranging the resultant equations. We have extract unknown coefficients in the system using Maple software and by plugging them into the original equation new soliton solutions to the equation are obtained. The findings show that the soliton solutions generated by these methods are valid. For illustrative purposes, we provide both 3-D and 2-D graphical representations. The strategy described in this research is superior to certain others that have been used to solve the same equation in the literature, according to computational findings. It demonstrates how these answers may be very helpful in comprehending physical processes in a range of applied mathematics fields.