On the lump interaction phenomena to the conformable fractional (2+1)-dimensional KdV equation

Abstract

This article pays attention to the interaction of waves for the (2+1)-dimensional KdV equation arising in the diversity of fields with the properties of conformable fractional derivatives. The KdV equation is notably significant as a prototypical example of an exactly solvable nonlinear system (that is, an infinite-dimensional system that is completely integrable). In a density-stratified ocean, the KdV equation characterizes shallow water waves that interact weakly and nonlinearly with long internal waves. The Hirota bilinear method (HBM) is successfully adopted with different test approaches. Different kinds of solutions like lump-periodic, breather-type, and two-wave solutions, have been obtained. The method used adequately describes NLPDEs since it both provides solutions that were previously confirmed and generates fresh exact solutions by combining the results of several operations. We also plot the graphs using the corresponding parameter values to demonstrate the graphical representation of selected solutions. These findings demonstrate the beneficial effects of the approach in improving the system’s nonlinear dynamical behavior. The outcomes demonstrate the efficiency, swiftness, ease, and adaptability of the used algorithm, even when applied to intricate systems.