This research employs recent and precise computational techniques to identify new and accurate solitary wave solutions of the modified Korteweg-de Vries-Kadomtsev-Petviashvili (KdV-KP) equation. The KdV-KP equation is a nonlinear partial differential equation that characterizes the evolution of waves in diverse physical systems, including nonlinear optics, fluid dynamics, and plasma physics. The equation generalizes the KdV and KP equations, which are fundamental models in their respective fields. Physically, the modified KdV-KP equation describes wave propagation where the effects of nonlinearity and dispersion can produce intriguing and complicated wave phenomena such as wave turbulence and solitary waves. The equation has numerous real-world applications, including modeling shallow water waves such as tsunamis and river waves in fluid dynamics, describing the behavior of plasma waves in fusion reactors and astrophysical plasmas, and studying the propagation of light in nonlinear media such as optical fibers in nonlinear optics. One of the most significant applications of the equation is in the study of solitons, which are self-sustaining solitary waves that preserve their shape and velocity even after colliding with other solitons. Solitons are used in various applications such as optical communications, where they transmit information over long distances without distortion, and in fluid dynamics, where they model long-lasting waves in the ocean. The study’s importance lies in its impact on the utilization of the modified KdV-KP equation in diverse fields of physics, including fluid dynamics and plasma physics. The effectiveness of the proposed techniques is demonstrated by comparing them with other computational methods, indicating their superiority.