Generalized variational principles of the Benney-Lin equation arising in fluid dynamics
Kang‐Jia Wang, Jianfang Wang
Abstract
Abstract 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.
Topics & Concepts
Variational principlePartial differential equationConservation lawWork (physics)First-order partial differential equationMathematicsNonlinear systemDifferential equationLuke's variational principleApplied mathematicsMathematical analysisClassical mechanicsPhysicsHamilton's principleEquations of motionThermodynamicsQuantum mechanicsFractional Differential Equations SolutionsNanofluid Flow and Heat TransferNonlinear Waves and Solitons