Lie symmetry analysis, power series solutions and conservation laws of time fractional coupled Boussinesq-Whitham-Broer-Kaup equations

10.30495/maca.2024.2046051.1114
Volume 6, Issue 3
Autumn 2024
Pages 79-94

Document Type : Original Article

Authors

School of Science, Wuhan University of Science and Technology, Wuhan 430081, Hubei, China

Abstract
 In this paper, the Lie symmetry analysis method is applied to time-fractional coupled Boussinesq-Whitham-Broer-Kaup equations, an important physics model. The obtained Lie symmetries are utilized to reduce the system of fractional partial differential equations with Riemann-Liouville fractional derivative to the system of fractional ordinary differential equations with Erdelyi-Kober fractional derivative. Then the power series method is applied to derive explicit power series solutions for the reduced system. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equations studied.

Keywords

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  • Receive Date 18 November 2024
  • Revise Date 19 December 2024
  • Accept Date 20 December 2024