Wave solutions of the DMBBM equation and the cKG equation using the simple equation method
Jiraporn Sanjun, Aungkanaporn Chankaew
Abstract
In this article, we transform the (1 + 1)-dimensional non-linear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and the (2 + 1)-dimensional cubic Klein Gordon (cKG) equation, which are the non-linear partial differential equations, into the non-linear ordinary differential equations by using the traveling wave transformation and solve these solutions with the simple equation method (SEM) with the Bernoulli equation. Two classes of exact explicit solutions-hyperbolic and trigonometric solutions of the associated NLEEs are characterized with some free parameters; we obtain the kink waves and periodic waves.
Topics & Concepts
MathematicsFirst-order partial differential equationMathematical analysisRiccati equationPartial differential equationHyperbolic partial differential equationWave equationSimple (philosophy)Wave packetBernoulli's principleDifferential equationHyperbolic functionCharacteristic equationExact differential equationOrdinary differential equationFisher's equationDispersive partial differential equationTrigonometric functionsIntegro-differential equationIndependent equationPhysicsGeometryThermodynamicsPhilosophyQuantum mechanicsEpistemologyNonlinear Waves and SolitonsNonlinear Photonic SystemsQuantum Mechanics and Non-Hermitian Physics