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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mi>G</mml:mi> <mml:mi>′</mml:mi> <mml:mo>/</mml:mo> <mml:mi>G</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>−</mml:mo> </mml:math> expansion scheme are utilized. As a consequence, various solutions of the exact solitons including, singular, singular-bright, periodic, dark, dark-bright, 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.