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A unique computational investigation of the exact traveling wave solutions for the fractional-order Kaup-Boussinesq and generalized Hirota Satsuma coupled KdV systems arising from water waves and interaction of long waves

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Abstract

A novel technique, named auxiliary equation method, is applied in this research work for obtaining new traveling wave solutions for two interesting proposed systems: the Kaup-Boussinesq system and generalized Hirota-Satsuma coupled KdV system with beta time fractional derivative. Our solutions were obtained using MAPLE software. This technique shows a great potential to be applied in solving various nonlinear fractional differential equations arising from mathematical physics and ocean engineering. Since a standard equation has not been used as an auxiliary equation for this technique, different and novel solutions are obtained via this technique.

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2022-01-01

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Auxiliary equation method | Beta derivative | Fractional differential equations | Nonlinear equations | Solitary solutions | Symbolic computation

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