New graphical observations for KdV equation and KdV–Burgers equation using modified auxiliary equation method
Ghazala Akram, Maasoomah Sadaf, Iqra Zainab
Abstract
This study is made to extract the exact solutions of Korteweg–de Vries–Burgers (KdVB) equation and Korteweg–de Vries (KdV) equation. The original idea of this work is to investigate KdV equation and KdVB equation for possible closed form solutions by employing the modified auxiliary equation (MAE) method. Exact traveling wave solutions of the considered equations are retrieved in the form of trigonometric and hyperbolic functions. Kink, periodic and singular wave patterns are obtained from the constructed solutions. The graphical illustration of the wave solutions is presented using 3D-surface plots to acquire the understanding of physical behavior of the obtained results up to possible extent.
Topics & Concepts
Korteweg–de Vries equationBurgers' equationHyperbolic functionTrigonometryMathematicsKadomtsev–Petviashvili equationTrigonometric functionsMathematical analysisWork (physics)Riccati equationPartial differential equationPhysicsNonlinear systemGeometryThermodynamicsQuantum mechanicsNonlinear Waves and SolitonsNonlinear Photonic SystemsQuantum Mechanics and Non-Hermitian Physics