Abstract This paper focuses on the exact solutions and dynamical properties of a concatenation model encompassing several high-order nonlinear Schrodinger equations arising from optical fiber communication. To the best of our knowledge, existing literature has only considered subsystems of this model under highly restrictive parameter conditions, with external drives being indispensable to induce chaotic behavior. The present work addresses all parameter regimes of the amplitude equation without introducing any external forces. Firstly, the amplitude equation is factorized for a family of parameters via the trial equation method, and a series of exact solutions are derived. Furthermore, a novel phenomenon-namely, the insensitivity of initial values for exact solutions-is identified and discussed. Secondly, for other parameter cases, the amplitude equation is analyzed from both qualitative and numerical simulation perspectives, leading to the discovery of a variety of novel internal chaotic structures with distinct topological characteristics. In addition, the sensitivity of initial values, parameter stability, bifurcations, Lyapunov exponents, and linearization at equilibrium points are investigated in detail. Two degenerate cases, which exhibit abundant dynamical behaviors, are also presented separately. These results provide a more comprehensive understanding of the dynamical behaviors of the model.
Cheng-shi Liu (Thu,) studied this question.
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