Analysis of soliton phenomena in (2+1)-dimensional Nizhnik-Novikov-Veselov model via a modified analytical technique

Abstract

The present research applies an improved version of the modified Extended Direct Algebraic Method (mEDAM) called +mEDAM to examine soliton phenomena in a notable mathematical model, namely the (2+1)-dimensional Nizhnik-Novikov-Veselov Model (NNVM), which possesses potential applications in exponentially localized structure interactions. The generalized hyperbolic and trigonometric functions are used to disclose a variety of soliton solutions, including kinks, anti-kink, bell-shaped and periodic soliton. Some 3D graphs are plotted for visual representations of these solutions which highlight their adaptability. The results provide a basis for practical usage and expansions to related mathematical models or physical systems. They also expand our understanding of the NNVM's dynamics, providing insights into its behavior and prospective applications.

Keywords

• partial differential equations
• nizhnik-novikov-veselov model
• modified extended direct algebraic method
• variable transformation
• soliton
• incompressible fluid
• shallow water wave