Exploring plasma phenomena with the Nizhnik–Novikov–Veselov formula: Analyzing ion-acoustic waves, solitons, and shocks

This paper delves into the intricacies of the ($2+1$)-dimensional asymmetric Nizhnik–Novikov–Veselov ($𝔸\mathbb{N}\mathbb{N}𝕍$) 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 $𝔸\mathbb{N}\mathbb{N}𝕍$ 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 $𝔸\mathbb{N}\mathbb{N}𝕍$ 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.