Novel soliton and wave solutions of a higher-dimensional fractional model in fluid mechanics

Abstract In this study, the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mn>4</m:mn> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> {(4\kern-1.0pt+\kern-1.0pt1)} -dimensional fractional Boiti–Leon–Manna–Pempinelli (BLMP) equation is considered to be an essential model for the incompressible fluid. The <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mi>m</m:mi> <m:mo>+</m:mo> <m:mfrac> <m:mn>1</m:mn> <m:msup> <m:mi>G</m:mi> <m:mo>′</m:mo> </m:msup> </m:mfrac> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> {(m+\frac{1}{G^{\prime}})} -expansion method which is an effective analytical method is employed to investigate the exact wave solutions of the equation mentioned above. The proposed scheme has provided various new types of exact solutions and it has not been applied before to the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mn>4</m:mn> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> {(4\kern-1.0pt+\kern-1.0pt1)} -dimensional BLMP equation with hyperbolic local derivative. These novel solutions can be observed as kink and singular solitons to describe wave propagation in fluid mechanics or continuum mechanics by selecting the suitable parameters and may find potential applications in modeling fluid motion phenomena such as tsunami propagation, ocean surface wave dynamics, and wave-current interactions in marine engineering. The exact wave structures have been revealed and compared employing the hyperbolic local derivative which is newly defined in the literature. The emerged solutions have also been corroborated via the computational software Mathematica and these results have been observed in 2D and 3D graphics.