Analysis of fractional solitary wave propagation with parametric effects and qualitative analysis of the modified Korteweg-de Vries-Kadomtsev-Petviashvili equation

This study explores the fractional form of modified Korteweg-de Vries-Kadomtsev-Petviashvili equation. This equation offers the physical description of how waves propagate and explains how nonlinearity and dispersion may lead to complex and fascinating wave phenomena arising in the diversity of fields like optical fibers, fluid dynamics, plasma waves, and shallow water waves. A variety of solutions in different shapes like bright, dark, singular, and combo solitary wave solutions have been extracted. Two recently developed integration tools known as generalized Arnous method and enhanced modified extended tanh-expansion method have been applied to secure the wave structures. Moreover, the physical significance of obtained solutions is meticulously analyzed by presenting a variety of graphs that illustrate the behaviour of the solutions for specific parameter values and a comprehensive investigation into the influence of the nonlinear parameter on the propagation of the solitary wave have been observed. Further, the governing equation is discussed for the qualitative analysis by the assistance of the Galilean transformation. Chaotic behavior is investigated by introducing a perturbed term in the dynamical system and presenting various analyses, including Poincare maps, time series, 2-dimensional 3-dimensional phase portraits. Moreover, chaotic attractor and sensitivity analysis are also observed. Our findings affirm the reliability of the applied techniques and suggest its potential application in future endeavours to uncover diverse and novel soliton solutions for other nonlinear evolution equations encountered in the realms of mathematical physics and engineering.