No abstract

No abstract

In this paper, we investigate the bright solitons on a cnoidal wave background train of the inhomogeneous nonlinear Schrödinger equation, which may be applicable to many physically realizable systems such as Bose–Einstein condensation media and plasma, etc. We use well-known methods to reduce the inhomogeneous nonlinear Schrödinger equation to a standard nonlinear Schrödinger equation by using the combination of Husimi's and Lens-type transformations. We study the superposed configuration of soliton with a cnoidal wave solution of the underlying equation. Finally, we discuss the dynamics of soliton on a cnoidal wave background in Bose–Einstein condensation trapped in linear density and harmonic density profiles separately.

The Hyers-Ulam stability of the Ordinary Differential Equations has been investigated and the investigation is ongoing. In this paper, by applying initial condition, we investigate the approximate solutions of the homogeneous and non-homogeneous linear differential equation in the sense of Hyers-Ulam-Rassias.

In this paper, we introduce a new integral transform, namely Aboodh transform, and we apply the transform to investigate the Hyers–Ulam stability, Hyers–Ulam–Rassias stability, Mittag-Leffler–Hyers–Ulam stability, and Mittag-Leffler–Hyers–Ulam–Rassias stability of second order linear differential equations.