Exact Solutions of Nonlinear Partial Differential Equations Using the Extended Kudryashov Method and Some Properties
Jian Zhou, Long Ju, Shiyin Zhao, Yufeng Zhang
Abstract
In this paper, we consider how to find new exact solutions for nonlinear partial differential equations using the extended Kudryashov method. This method mainly uses the Riccati equation and the Bernoulli equation where there are some underdetermined constant parameters. And we also use the concept of symmetry to study its reduction equation, Lie transformation group, self-adjointness, and conservation laws. This paper mainly studies the Boussinesq class and the shallow water wave equation in (1 + 1) dimensions and tries to find new exact solutions and symmetry properties of them.
Topics & Concepts
Riccati equationSymmetry (geometry)Partial differential equationUnderdetermined systemMathematicsTransformation (genetics)Nonlinear systemConservation lawApplied mathematicsOrdinary differential equationClass (philosophy)Mathematical analysisDifferential equationPhysicsComputer scienceGeometryGeneChemistryBiochemistryQuantum mechanicsArtificial intelligenceNonlinear Waves and SolitonsNonlinear Photonic SystemsFractional Differential Equations Solutions