Abundant exact solutions to a generalized nonlinear Schrödinger equation with local fractional derivative. (14th March 2021)

• Record Type: Journal Article
• Authors: Ghanbari, Behzad
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 11(2021)
• Page Start: 8759
• Page End: 8774
• Publication Date: 2021-03-14
• Subjects: exact solutions -- fractals -- fractional derivatives and integrals -- local fractional operators; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7302
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The paper aims to employ a new effective methodology to build exact fractional solutions to the generalized nonlinear Schrödinger equation with a local fractional operator defined on Cantor sets. The equation contains group velocity dispersion and second‐order spatiotemporal dispersion coefficients. We obtain exact solutions of the equation via the generalized version of the exponential rational function method. This new version of the method uses a set of elementary functions that are adopted on the contour set. To study the dynamic behavior of the obtained results, extensive numerical simulations are provided. We observe that the employed method is simple but quite efficient for determining the exact solutions of the problem in the local sense. Moreover, they are practically compatible with solving various classes of nonlinear problems arising in mathematical physics. All computations are carried out using the Maple package.