Exact Traveling Waves of a Generalized Scale-Invariant Analogue of the Korteweg–de Vries Equation
Lewa’ Alzaleq, V.S. Manoranjan, Baha Alzalg
Abstract
In this paper, we study a generalized scale-invariant analogue of the well-known Korteweg–de Vries (KdV) equation. This generalized equation can be thought of as a bridge between the KdV equation and the SIdV equation that was discovered recently, and shares the same one-soliton solution as the KdV equation. By employing the auxiliary equation method, we are able to obtain a wide variety of traveling wave solutions, both bounded and singular, which are kink and bell types, periodic waves, exponential waves, and peaked (peakon) waves. As far as we know, these solutions are new and their explicit closed-form expressions have not been reported elsewhere in the literature.
Topics & Concepts
Korteweg–de Vries equationPeakonTraveling waveInvariant (physics)Exponential functionMathematicsMathematical analysisDispersionless equationKadomtsev–Petviashvili equationSolitonBounded functionMathematical physicsPhysicsBurgers' equationNonlinear systemPartial differential equationIntegrable systemQuantum mechanicsNonlinear Waves and SolitonsNonlinear Photonic SystemsFractional Differential Equations Solutions