Lie point symmetries, conservation laws, and analytical solutions of a generalized time-fractional Sawada–Kotera equation

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Abstract
Under investigation in this work is the invariance properties of the time-fractional generalized Sawada–Kotera equation, which can describe motion of long waves in shallow water under gravity and in a one-dimensional nonlinear lattice. With the help of the Lie symmetry analysis method of fractional differential equations, we strictly derive the vector fields and symmetry reductions of the equation. Furthermore, based on the power series theory, an effective method is presented to succinctly construct its analytical solutions. Finally, using the new conservation theorem, the conservation laws of the equation are well constructed with a detailed derivation.
Funding Information
  • China Postdoctoral Science Foundation (2017T100413, 2015M570498)
  • National Natural Science Foundation of China (51522902, 51379033, 11301527, 51579040)
  • Fundamental Research Funds for the Central Universities (2017XKQY101,DUT17ZD233)
  • Ministry of Industry and Information Technology of China
  • General Financial Grant from the China Postdoctoral Science Foundation (2017T100413, 2015M570498)

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