SYMMETRY ANALYSIS FOR A SEVENTH-ORDER GENERALIZED KdV EQUATION AND ITS FRACTIONAL VERSION IN FLUID MECHANICS
Gangwei Wang, Peng Li, Yanbin Wu, Xing Su
Abstract
KdV types of equations play an important role in many fields. In this paper, we study a seventh-order generalized KdV equation and its fractional version in fluid mechanics using symmetry. From symmetry, the corresponding vectors, symmetry reduction and conservation laws are derived. Potential equation is also analyzed with regard to the symmetry method. Based on the symmetry, similarity reductions and conservation laws are also presented. Subsequently, the fractional version of the seventh-order KdV equation is discussed. Finally, differential invariants are constructed for the special case.
Topics & Concepts
Korteweg–de Vries equationSymmetry (geometry)Conservation lawMathematicsPartial differential equationMathematical physicsOrder (exchange)Differential equationMathematical analysisApplied mathematicsPhysicsQuantum mechanicsNonlinear systemGeometryEconomicsFinanceNonlinear Waves and SolitonsFractional Differential Equations SolutionsNonlinear Photonic Systems