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This paper investigates the optical soliton solutions of the Lakshmanan–Porsezian–Daniel equation, a nonlinear evolution equation modeling the propagation of optical soliton waves in materials influenced by parabolic law nonlinearity and spatio-temporal dispersion. Employing both the Kudryashov and new Kudryashov methods, the study captures various soliton waves, deriving both dark and bright soliton solutions. The research delves into the effects of the model parameters on these solutions, presenting the findings through detailed 3D and 2D simulation images. Practical and rapid results achieved using both Kudryashov methods are highlighted, positioning this work as a valuable reference for peers. The study's distinct combination of the Lakshmanan–Porsezian–Daniel equation and the chosen analytical techniques not only introduces novelty but also emphasizes practicality and efficiency. This innovative approach, coupled with its significant contribution to the knowledge base, underscores the research's relevance in the field. [ABSTRACT FROM AUTHOR]

This paper presents the modulation instability (MI) analysis and the different types of optical soliton solutions of the Triki–Biswas model equation. The aforesaid model equation is the generalization of the derivative nonlinear Schrödinger equation which describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel efficient integration scheme. During this work, a sequence of optical solitons is produced that may have an important in optical fiber systems. The results show that the studied model hypothetically has incredibly rich optical soliton solutions. The constraint conditions for valid soliton solutions are also reported. The gained results show that the applied method is efficient, powerful and can be applied to various complex models with the help of representative calculations. [ABSTRACT FROM AUTHOR]

This study consider Gerdjikov-Ivanov equation where the perturbation terms appear with full non-linearity. The Jacobi elliptic function ansatz method is implemented to obtain exact solutions of this equation that models pulse dynamics in optical fibers. It is retrieved some bright, dark optical and singular solitons profile in the limiting cases of the Jacobi elliptic functions. The constraint conditions depending on the parameters for the existence of solitons are also presented. [ABSTRACT FROM AUTHOR]