Investigation of exact solitons to the quartic Rosenau-Kawahara-Regularized-Long-Wave fluid model with fractional derivative and qualitative analysis

Abstract

In this research, the exact solitons to an important wave equation, namely, the
quartic Rosenau-Kawahara-Regularized-Long-Wave (QRKRLW) equation are obtained
along with an effective definition of fractional derivative, Truncated M-fractional. This
model has much importance in 
fluid dynamics, shallow waves, and many others. For
our this purpose, two effective schemes, the modified extended tanh function scheme
and the improved (G'/G)-expansion scheme are utilized. As a consequence, various
solutions of the exact solitons including, singular, singular-bright, periodic, dark, darkbright,
and others are obtained. To verify and to represent the solutions, we plotted
the solutions through 2D, 3D, and contour plots using Mathematica tool. Additionally, the qualitative analysis in the concept of stability analysis and modulation instability
analysis is performed for verifying the being exact and accurate solutions. At the
end, the schemes are also useful for the other nonlinear models in various branches of
sciences, and engineering.