MAEJO INTERNATIONAL JOURNAL OF SCIENCE & TECHNOLOGY

Volume 16, No. 03, Month SEPTEMBER, Year 2022, Pages 262 - 274

Effects of wave solutions on shallow-water equation, optical- fibre equation and electric-circuit equation

Weerachai Thadee, Aungkanaporn Chankaew, Sirasrete Phoosree

Abstract Download PDF

The fractional non-linearity of space-and-time of Estevez-Mansfield-Clarkson equation, Ablowitz-Kaup-Newell-Segur equation and modified Korteweg-de Vries equation reveals the effects on shallow-water waves, optical-fibre waves and electric-circuit waves respectively. Using the fractional derivative of Jumarie"es Riemann-Liouville and a combination of Kudryashov method and the process of establishing the answer in finite series, the procedure is called the transformation of fractional non-linearity of partial differential equations into the non-linearity of ordinary differential equations. The newly discovered analytical solutions take the form of exponential functions, which ultimately leads to the occurrence of physical wave effects. These effects are manifested in kink and periodic waves, and they are separately depicted by 2-D, 3-D and contour graphs.

Keywords

wave solutions, fractional Estevez-Mansfield-Clarkson equation, fractional Ablowitz-Kaup-Newell-Segur equation, fractional modified Korteweg-de Vries equation, Kudryashov method

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