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Time-fractional Hirota equation; fractional complex transform; complete discrimination system; tanhexpansion; travelling wave

In this article, we have developed new exact analytical solutions of a nonlinear evolution equation that appear in mathematical physics, a (2 + 1)-dimensional generalised time-fractional Hirota equation, which describes the wave propagation in an erbium-doped nonlinear fibre with higher-order dispersion. By virtue of the tanh-expansion and complete discrimination system by means of fractional complex transform, travelling wave solutions are derived.Wave interaction for the wave propagation strength and angle of field quantity under the long wave limit are analysed: Bell-shape solitons are found and it is found that the complex transform coefficient in thesystem affects the direction of the wave propagation, patterns of the soliton interaction, distance and direction.

YOUWEI ZHANG¹

1. School of Mathematics and Statistics, Hexi University, Beihuan Road, 846, Zhangye 734000, China

Published

1 March 2018

Manuscript received

24 July 2017

Manuscript revised

28 September 2017

Accepted

10 October 2017

Early published

Unedited version published online

Final version published online

9 February 2018