Soliton solutions and dynamical bifurcation analysis of the Yajima-Oikawa equations

Abstract

The Yajima–Oikawa equations describes the resonant interaction between ion sound waves and Langmuir waves in plasma. Despite its importance, the detailed dynamical behavior of this model has not been comprehensively explored. In this work, we present a unified analytical and dynamical framework that combines exact solution construction with qualitative and quantitative analysis. By employing traveling wave transformations together with the first integral method, a class of exact solutions in terms of Jacobi elliptic functions is derived. These solutions are systematically classified, according to bifurcation scenarios, into periodic, quasi-periodic, solitary, and kink-type wave structures. To investigate the global dynamics, an external periodic perturbation is introduced, transforming the system into a higher-dimensional dynamical model. This enables the study of transitions between regular and chaotic regimes. The presence of chaos is confirmed through phase portraits, Poincaré sections, time series analysis, and Lyapunov exponent calculations, while sensitivity to initial conditions is also examined. The results provide a deeper understanding of nonlinear wave interactions and reveal rich dynamical features of the classical Yajima–Oikawa equations. These findings are relevant for applications in plasma physics and related fields, where accurate prediction and control of wave dynamics are essential, including in plasma-based devices such as fusion systems and wave propagation technologies.