Exploration of soliton solutions and dynamic behaviors of various solitonic patterns in a concatenated model using a newly advanced generalized version of the sub-ODE method

In this work, we introduce a newly advanced generalized version of the sub-ODE method for constructing soliton solutions and illustrate the dynamic nature of various solitonic structures in a concatenated model, for the first time. We consider the recently proposed concatenated model, which combines the Lakshmanan-Porsezian-Daniel (LPD), Sasa-Satsuma (SS), and nonlinear Schrödinger’s equations. Numerous soliton solutions of the considered model are derived by applying the proposed method together with a traveling-wave reduction. In addition, several versions of the sub-ODE approach are employed, including the new modified sub-ODE method and the newly improved modified generalized sub-ODE method, to construct diverse classes of exact wave solutions. These unified and generalized approaches are utilized to construct novel soliton solutions and wave interactions for the concatenated model, using Computational software-Mathematica. Consequently, we have derived a plethora of exact solutions, namely, bright solitons, dark solitons, singular solitons, periodic wave solutions, Weierstrass elliptic function solutions, as well as Jacobi elliptic function solutions, and additional straddled soliton solutions of the considered model. We also provide the parameter constraints necessary for the existence of these solutions. Furthermore, we illustrate 3D and 2D figures of the acquired solutions for specific selections of arbitrary parameters. We demonstrate the effects of varying the nonlinear parameters of the concatenated model on the evolution of solitons. The solutions obtained in this study are significant for applications in nonlinear dynamics, computational fluid dynamics, plasma physics, and optical physics.