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This study introduces innovative analytical solutions for the (2+1)-dimensional nonlinear Jaulent–Miodek (핁필) equation, a governing model elucidating the propagation characteristics of nonlinear shallow water waves with finite amplitude. Employing analytical methodologies such as the Khater II and unified methods, alongside the Adomian decomposition method as a semi-analytical approach, series solutions are derived with the primary aim of elucidating the fundamental physics dictating the evolution of 핁필 waves. Within the realm of nonlinear fluid dynamics, the 핁필 equation encapsulates the behavior of irrotational, inviscid, and incompressible fluid flow, wherein nonlinear effects and dispersion intricately balance to yield stable propagating waves. This equation encompasses terms representing nonlinear convection, dispersion, and nonlinearity effects. The analytical methodologies employed in this investigation yield solutions for various instances of the 핁필 equation, demonstrating convergence, accuracy, and computational efficiency. The outcomes reveal that the Adomian decomposition method yields solutions congruent with those obtained through analytical techniques, thereby affirming the precision of the derived solutions. Furthermore, this study advances the comprehension of the physical implications inherent in the 핁필 equation, serving as a benchmark for evaluating alternative methodologies. The analytical approaches elucidated in this research furnish accessible tools for addressing a diverse array of nonlinear wave equations in mathematical physics and engineering domains. In summary, the introduction of novel exact and approximate solutions significantly contributes to the advancement of knowledge pertaining to the (2+1)-dimensional 핁필 equation. The ramifications of this research extend to the modeling of shallow water waves, offering invaluable insights for researchers and practitioners engaged in the field. [ABSTRACT FROM AUTHOR]

This paper delves into the intricacies of the (2+1)-dimensional asymmetric Nizhnik–Novikov–Veselov (픸ℕℕ핍) model, a nonlinear partial differential equation governing ion-acoustic wave propagation in plasma. By employing advanced analytical and numerical approaches, the study explores innovative solitary wave solutions, particularly focusing on the dynamics of isochoric flow. Isochoric flow analysis is crucial for unraveling the complex behaviors exhibited by incompressible fluids like elastomers and bio-elastomers, which maintain a constant density.The derivation of the (2+1)-dimensional 픸ℕℕ핍 equation stems from fluid equations governing plasma dynamics. This model serves as a valuable tool for simulating experimental observations of plasma waves. The computational methodology applied in this research demonstrates a commendable level of precision and consistency, yielding novel solitary wave solutions previously unreported in the 픸ℕℕ핍 model. These results underscore the study’s importance and novelty.The outcomes not only contribute to our understanding of incompressible fluid dynamics, but also lay the groundwork for future investigations in this domain. The revealed solitary wave solutions have the potential to inform the development of more accurate models for predicting fluid dynamics, thereby advancing the field. [ABSTRACT FROM AUTHOR]