Travelling wave solutions of the third-order KdV equation using Jacobi elliptic function method
Jamil Abbas Haider, S. Asghar, S. Nadeem
Abstract
For the purpose of constructing the exact periodic solutions of nonlinear wave equations, it has been proposed to use a method known as the Jacobi elliptic function expansion method. This method is more general than the hyperbolic tangent function expansion method. It has been demonstrated that the periodic solutions obtained using this method contain both solitary wave solutions and shock wave solutions in some instances.
Topics & Concepts
Elliptic functionHyperbolic functionCnoidal wavePeriodic waveJacobi elliptic functionsKorteweg–de Vries equationMathematical analysisNonlinear systemTraveling waveFunction (biology)Shock waveTangentThird orderOrder (exchange)MathematicsApplied mathematicsWave equationPhysicsGeometryFinancePhilosophyBiologyEvolutionary biologyEconomicsTheologyQuantum mechanicsThermodynamicsNonlinear Waves and SolitonsNonlinear Photonic SystemsAdvanced Mathematical Physics Problems