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In this paper, the modulation instability (MI) of a (1 + 1) -dimensional nonlocal nonlinear Schrödinger equation with general polynomial law nonlinearity and an external potential is investigated. Some new dark and bright soliton solutions are obtained for polynomial law nonlinearities of third and fifth orders. [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 paper investigates the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain (HMF) model. The model describes the nonlinear spin dynamics of HMF. By adopting the modified F -Expansion and projective Riccati equation methods, we report the dark, combined dark-bright and envelope optical solitons, complexitons singular solutions of the equation along with the conditions that must be satisfied for solitons to exist. The physical structure of the obtained solutions are shown by graphic illustration in order to give a better understanding on the dynamics of optical solitons. [ABSTRACT FROM AUTHOR]

In this study, two integration techniques are employed to reach optical solitons to the (n + 1) -dimensional nonlinear Schrödinger's equation ((n + 1) -NLSE) with Kerr and power laws nonlinearities. These are the undetermined coefficient and Bernoulli sub-ODE methods. We acquired bright, dark, and periodic singular soliton solutions. The necessary conditions for the existence of these solitons are presented. [ABSTRACT FROM AUTHOR]

This work studies the hyperbolic nonlinear Schrödinger equation (H-NLSE) in (2 + 1)-dimensions. The model describes the evolution of the elevation of water wave surface for slowly modulated wave trains in deep water in hydrodynamics, and also governs the propagation of electromagnetic fields in self-focusing and normally dispersive planar wave guides in optics. A class of gray and black optical solitary wave solutions of the H-NLSE are reported by adopting an appropriate solitary wave ansatz solution. Moreover, classification of conservation laws (Cls) to the H-NLSE is implemented using the multipliers approach. Some physical interpretations and analysis of the results obtained are also presented. [ABSTRACT FROM AUTHOR]