A new computational investigation to the new exact solutions of (3 + 1)-dimensional WKdV equations via two novel procedures arising in shallow water magnetohydrodynamics

Abstract

Abstract Various new exact solutions to <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mn>3</m:mn> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> \left(3+1) -dimensional Wazwaz–KdV equations are obtained in this work via two techniques: the modified Kudryashov procedure and modified simple equation method. The 3D plots, contour plots, and 2D plots of some obtained solutions are provided to describe the dynamic characteristics of the obtained solutions. Our employed techniques are very helpful in constructing new exact solutions to several nonlinear models encountered in ocean scientific phenomena arising in stratified flows, shallow water, plasma physics, and internal waves.