On traveling wave solutions of a class of KdV-Burgers-Kuramoto type equations

Yanxia Hu; Qian Liu; Yanxia Hu; Qian Liu

doi:10.3934/math.2019.5.1450

AIMS Mathematics

2019, Volume 4, Issue 5: 1450-1465. doi: 10.3934/math.2019.5.1450

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Research article

On traveling wave solutions of a class of KdV-Burgers-Kuramoto type equations

Yanxia Hu ^,,
Qian Liu

School of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China

Received: 21 May 2019 Accepted: 25 August 2019 Published: 20 September 2019
MSC : 34A05, 34A34

In the paper, the traveling wave solutions of a KdV–Burgers-Kuramoto type equation with arbitrary power nonlinearity are considered. Lie symmetry analysis method on the equation is performed, which shows that the equation possesses traveling wave solutions. By qualitative analysing the equivalent autonomous system of the traveling wave equation of the equation, the existence of the traveling wave solutions of the equation is presented. Through analysing the associated determining system, the non-trivial infinitesimal generator of Lie symmetry admitted by the traveling wave solutions equation under the certain parametric conditions is found. The traveling wave solutions of the KdV–Burgers-Kuramoto type equation by solving the invariant surface condition equation under the certain parametric conditions are obtained.
- KdV-Burgers-Kuramoto type equation,
- qualitative analysis,
- traveling wave solutions,
- Lie symmetry group
Citation: Yanxia Hu, Qian Liu. On traveling wave solutions of a class of KdV-Burgers-Kuramoto type equations[J]. AIMS Mathematics, 2019, 4(5): 1450-1465. doi: 10.3934/math.2019.5.1450

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Abstract

In the paper, the traveling wave solutions of a KdV–Burgers-Kuramoto type equation with arbitrary power nonlinearity are considered. Lie symmetry analysis method on the equation is performed, which shows that the equation possesses traveling wave solutions. By qualitative analysing the equivalent autonomous system of the traveling wave equation of the equation, the existence of the traveling wave solutions of the equation is presented. Through analysing the associated determining system, the non-trivial infinitesimal generator of Lie symmetry admitted by the traveling wave solutions equation under the certain parametric conditions is found. The traveling wave solutions of the KdV–Burgers-Kuramoto type equation by solving the invariant surface condition equation under the certain parametric conditions are obtained.

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