A comprehensive analytical study of solitons and nonlinear dynamics in a concatenated DNLS-type model

In mathematical physics, such as nuclear physics, fluid dynamics, quantum optics, and plasma physics, nonlinear evolution equations are essential. The concatenation model, that was first presented in 2014 and has attracted a lot of interest in nonlinear optics, comes in two varieties: the dispersive concatenation model and the standard concatenation model. Both models are made by merging basic integrable components. This work investigates the solitonic structures and nonlinear dynamics of a concatenated DNSL model from plasma physics, which consists primarily of the Kaup–Newell, Chen–Lee–Liu, and Gerdjikov–Ivanov equations. Using a suitable traveling-wave transformation, the PDE is transformed into an ordinary differential equation, and the Modified Sardar Sub-Equation method produces exact trigonometric and hyperbolic soliton solutions. A thorough dynamical analysis is carried out in order to supplement the analytical solutions. Chaotic behavior is examined using Poincaré maps, return maps with fractal dimensions (box-counting and correlation-sum methods), power spectrum, bifurcation diagram, Lyapunov exponents, time series and 3D strange attractor analysis. The results indicate rich nonlinear dynamics and several families of soliton solutions, illustrating the mathematical complexity and physical importance of the proposed model.