Optical solitons, nonlinear self-adjointness and conservation laws for the cubic nonlinear Shrödinger's equation with repulsive delta potential

• Published in: Superlattices and microstructures Vol. 111; pp. 546 - 555
• Main Authors: Baleanu, Dumitru, Inc, Mustafa, Aliyu, Aliyu Isa, Yusuf, Abdullahi
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2017
• Subjects: Cls; Complex envelope function ansatz; Soliton; δ−NLSE; Soliton; Complex envelope function ansatz; Cls; δ−NLSE
• ISSN: 0749-6036; 1096-3677
• DOI: 10.1016/j.spmi.2017.07.010

In this paper, the complex envelope function ansatz method is used to acquire the optical solitons to the cubic nonlinear Shrödinger's equation with repulsive delta potential (δ−NLSE). The method reveals dark and bright optical solitons. The necessary constraint conditions which guarantee the existence of the solitons are also presented. We studied the δ−NLSE by analyzing a system of partial differential equations (PDEs) obtained by decomposing the equation into real and imaginary components. We derive the Lie point symmetry generators of the system and prove that the system is nonlinearly self-adjoint with an explicit form of a differential substitution satisfying the nonlinear self-adjoint condition. Then we use these facts to establish a set of conserved vectors for the system using the general Cls theorem presented by Ibragimov. Some interesting figures for the acquired solutions are also presented. •The Cubic Nonlinear Shrödinger's equation with Repulsive Delta Potential are studied.•Some new optical solitons are constructed by using the complex envelope function ansatz method and Lie symmetry.•Some interesting figures for the acquired solutions are also presented.