Analyzing novel soliton configurations and stability characteristics in a (3+1)-dimensional Hirota bilinear fluid model

Badshah F., Tariq K. U., Alhefthi R. K., Tufail R. N.

European Physical Journal Plus, vol.141, no.8, 2026 (SCI-Expanded, Scopus)

Abstract

This paper presents a comprehensive investigation of a new (3+1)-dimensional Hirota bilinear model arising in fluid mechanics. We begin by constructing the bilinear representation of the governing equation using the Hirota bilinear formalism. A range of exact solutions is then derived. These include periodic wave solitons, lump interactions with stripy and double stripy solitons, periodic solutions interacting with double stripy solitons, and lump collisions with periodic waves. A couple of distinct approaches are used to achieve traveling wave solutions: the improved F-expansion algorithm and the modified extended tanh-function method. We analyze these computations with numerical simulations utilizing the Adomian decomposition approach, quantifying absolute errors by comparing approximate and exact solutions. Stability and modulation instability of the model are also examined, and we confirm that the traveling wave solutions are stable under small perturbations. To illustrate the physical features of the solutions, we present two-dimensional, contour, and three-dimensional plots. These reveal a diverse family of soliton profiles, including trigonometric, bright, hyperbolic, rational, dark (V-shaped), periodic, and singular bell-type structures. We believe the results reported here are novel and may prove useful for analyzing other higher-dimensional nonlinear evolution equations.