Analysis of truncated M-fractional (2+1)-dimensional Kadomtsev-Petviashvili-modified equal-width model via a new adaptation of an analytical technique

Abstract

This study emphasizes the construction of various types of solitary wave solutions of the M-truncated fractional (2 + 1)-dimensional Kadomtsev-Petviashvili-modified equal-width (KPmEW) equation, which models various long-wavelength phenomena, such as water waves, ferromagnetic waves, and matter-wave pulses. A modified form of the trial equation method is employed to investigate the wave structures of the proposed fractional nonlinear model. Through this approach, a wide spectrum of rational, exponential, hyperbolic, and Jacobi elliptic function solutions is derived. The corresponding wave profiles are visualized in two and three dimensions to elucidate their physical characteristics. The analytical findings are verified using the symbolic software Mathematica. The obtained results extend previous studies and provide new insights into the dynamic behaviour of fractional nonlinear evolution equations.