ABUNDANT SOLITONS SOLUTIONS OF THE (2+1)-DIMENSIONAL KADOMTSEV- PETVIASHVILI-MODIFIED EQUAL WIDTH MODEL

Analytical soliton solutions refer to mathematical expressions that articulate stable, localized waves in firm nonlinear partial differential equations. The primary aim of the current investigation is to compile the plenty of forms of soliton solutions for the Kadomtsev–Petviashvili-modified equal width (KP-mEW) model using the extended direct algebraic method (EDAM) and the new mapping method (NMM), which require waves in ferromagnetic materials, water waves with long wavelengths and dispersed frequencies, and slightly nonlinear reinstating forces. The accompanying solutions are discovered to be mixed M-shaped soliton, hyperbolic, trigonometric, periodic, peakon and anti-peakon, combined bright-dark, kink, bell and anti-bell-shaped, compacton and W-shaped solitons, and these solutions are illustrated graphically employing 2D, 3D, and contour profiles. Plotting and validity examination of the discovered soliton solutions take place using the Wolfram Mathematica 14. The KP-mEW model is useful in soliton theory, providing a mathematical framework to study solitary wave solutions. Therefore, an extensive spectrum of further nonlinear systems can be explored with the current research methodology.