INVESTIGATION OF THE TIME FRACTIONAL GENERALIZED (2 + 1)-DIMENSIONAL ZAKHAROV–KUZNETSOV EQUATION WITH SINGLE-POWER LAW NONLINEARITY
Jian‐Gen Liu, Yufeng Zhang, Jingjing Wang
Abstract
In this paper, we studied the time fractional generalized [Formula: see text]-dimensional Zakharov–Kuznetsov (ZK) equation with single-power law nonlinearity, which can be used to describe weakly nonlinear ion-acoustic waves in strongly magnetized lossless plasma in two dimensions. Through the fractional Lie transformation group idea, the symmetries, similarity reduction, one-parameter Lie transformation group and conservation laws of these considered equations were obtained. In addition, some new exact solutions were also constructed for them. These novel results provide a new perspective for studying the evolutionary mechanism of these considered models.
Topics & Concepts
Conservation lawNonlinear systemHomogeneous spaceTransformation (genetics)MathematicsFractional calculusReduction (mathematics)Power (physics)Similarity (geometry)Symmetry (geometry)Mathematical analysisMathematical physicsApplied mathematicsPhysicsComputer scienceQuantum mechanicsGeometryImage (mathematics)GeneArtificial intelligenceBiochemistryChemistryNonlinear Waves and SolitonsFractional Differential Equations SolutionsNonlinear Photonic Systems