Generalized variational principles of the Benney-Lin equation arising in fluid dynamics

Generalized variational principles of the Benney-Lin equation arising in fluid dynamics

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 stud...

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Veröffentlicht in:Europhysics letters 2022-08, Vol.139 (3), p.33006
Hauptverfasser: Wang, Kang-Jia, Wang, Jian-Fang
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Sprache:eng
Schlagworte:
Conservation laws
Dynamic structural analysis
Fluid dynamics
Inverse method
Nonlinear differential equations
Nonlinear dynamics
Partial differential equations
Variational principles
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description 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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subjects Conservation laws
Dynamic structural analysis
Fluid dynamics
Inverse method
Nonlinear differential equations
Nonlinear dynamics
Partial differential equations
Variational principles
title Generalized variational principles of the Benney-Lin equation arising in fluid dynamics
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