Lie symmetries, exact solutions and conservation laws of time fractional Boussinesq–Burgers system in ocean waves  

作　　者：Jicheng Yu Yuqiang Feng 

机构地区：[1]School of Science,Wuhan University of Science and Technology,Wuhan 430081,Hubei,China [2]Hubei Province Key Laboratory of Systems Science in Metallurgical Process,Wuhan 430081,Hubei,China

出　　处：《Communications in Theoretical Physics》2024年第12期13-23,共11页理论物理通讯(英文版)

摘　　要：In this paper, the Lie symmetry analysis method is applied to the time-fractional Boussinesq–Burgers system which is used to describe shallow water waves near an ocean coast or in a lake.We obtain all the Lie symmetries admitted by the system and use them to reduce the fractional partial differential equations with a Riemann–Liouville fractional derivative to some fractional ordinary differential equations with an Erdélyi–Kober fractional derivative, thereby getting some exact solutions of the reduced equations. For power series solutions, we prove their convergence and show the dynamic analysis of their truncated graphs. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equations studied.

关 键 词：Lie symmetry analysis fractional Boussinesq-Burgers system Riemann-Liouville fractional derivative Erdélyi-Kober fractional derivative conservation laws 

分 类 号：O175.29[理学—数学]