On the variational principles of the Burgers-Korteweg-de Vries equation in fluid mechanics
Jinghua Liu, Yi-Ning Yang, Kang‐Jia Wang, Hong‐Wei Zhu
Abstract
Abstract As is known to all, it is extraordinarily difficult to construct the variational principles of the nonlinear partial differential equations (NPDEs) for fluid mechanics. In this work, we focus on the Burgers-Korteweg-de Vries equation and attempt to establish its generalized variational principle by employing the semi-inverse method (SIM). Two different generalized variational principles (GVPs) are extracted and the detailed derivation process is presented. The GVPs can present some new inspiration for the study and application of the variational method.
Topics & Concepts
Burgers' equationFluid mechanicsKorteweg–de Vries equationMathematical physicsContinuum mechanicsClassical mechanicsPhysicsMathematicsApplied mathematicsMathematical analysisMechanicsPartial differential equationNonlinear systemQuantum mechanicsExperimental and Theoretical Physics StudiesQuantum chaos and dynamical systemsNonlinear Waves and Solitons