Dynamic behavior of explicit elliptic and quasi periodic-wave solutions to the generalized [formula omitted]-dimensional Kundu–Mukherjee–Naskar equation

Abstract

This paper introduces novel explicit traveling solutions to the generalized (2+1)-dimensional Kundu–Mukherjee–Naskar equation, a model relevant in optical fiber pulses, fluid dynamics, medical imaging, and ocean rogue waves. We propose rational form functions that incorporate both sine and cosine variables or sinh and cosh variables as potential solutions to the model. Subsequently, we utilize 3D diagrams to visually illustrate the characteristics of the identified propagating solutions, which exhibit elliptic-periodic, convex-periodic, cusp-soliton, and quasi-periodic patterns. Furthermore, a graphical analysis is conducted to explore the impact of the model’s parameters; nonlinearity and dispersion. Additionally, we introduce a comparative analysis to assess the superiority of the proposed approach over other existing methods such as Kudryashov-expansion, sine-function, and tanh(coth)-expansion methods. We anticipate that the insights gained from this analysis will prove valuable for understanding and studying other nonlinear models.