10.30495/maca.2024.2046051.1114

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

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  • Jicheng Yu1,
  • Yuqiang Feng1,
  1. School of Science, Wuhan University of Science and Technology, Wuhan 430081, Hubei, China

Published in Issue 2024-09-01

How to Cite

Lie symmetry analysis, power series solutions and conservation laws of time fractional coupled Boussinesq-Whitham-Broer-Kaup equations. (2024). Mathematical Analysis and Its Contemporary Applications, 6(3). https://doi.org/10.30495/maca.2024.2046051.1114

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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 Erd´elyi-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

  • Lie symmetry analysis,
  • time fractional coupled Boussinesq-Whitham-Broer-Kaup equations,
  • Riemann-Liouville fractional derivative,
  • Erd´elyi-Kober fractional derivative,
  • conservation laws
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