Analytical novel solutions to the fractional optical dynamics in a medium with polynomial law nonlinearity and higher order dispersion with a new local fractional derivative. (English) Zbl 1479.78007

Summary: Novel solutions for the nonlinear dynamics of Schrödinger equation for polynomial law medium with third-order dispersion (TOD), fourth-order dispersion (FOD), and self-steepening are investigated based in a novel local fractional derivative of order \(\alpha\) and the Jacobi elliptic function method which are combined into a novel fractional sub-equation method. The Jacobi elliptic function method will provide different types of analytical solutions and not only soliton type solutions for the propagation of ultra-short optical signals through a polynomial law medium. Solutions are illustrated in 3-D graphs, contour plots and 2-D plots under the obtained constraint conditions.


78A40 Waves and radiation in optics and electromagnetic theory
78A48 Composite media; random media in optics and electromagnetic theory
35Q55 NLS equations (nonlinear Schrödinger equations)
81U30 Dispersion theory, dispersion relations arising in quantum theory
26A33 Fractional derivatives and integrals
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
Full Text: DOI


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