Volume 139, Number 3, August 2022
|Number of page(s)||4|
|Section||Fluid and nonlinear dynamics|
|Published online||08 August 2022|
Generalized variational principles of the Benney-Lin equation arising in fluid dynamics
1 School of Physics and Electronic Information Engineering, Henan Polytechnic University - Jiaozuo, 454003, China
2 School of Computer Science and Technology, Henan Polytechnic University - Jiaozuo, 454003, China
(a) email@example.com (corresponding author)
Received: 28 July 2021
Accepted: 24 November 2021
Variational principle is important since it can not only reveal the possible solution structures of the equation but also provide the conservation laws in an energy form. Unfortunately, not all the differential equations can find their variational forms. In this work, the Benney-Lin equation is studied and its two different generalized variational principles are successfully established by using the semi-inverse method. The derivation process is given in detail. The finding in this work is expected to give an insight into the study of the nonlinear partial differential equations arising in fluid dynamics.
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