Exact traveling wave solutions of the Schamel Burgers’ equation by using generalized-improved and generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1950" altimg="si4.svg"> <mml:mfenced open="(" close=")"> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>′</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:mfenced> </mml:math> expansion methods
Sanjaya K. Mohanty, O. V. Kravchenko, Apul N. Dev
Abstract
The Schamel Burgers’ equation is a nonlinear partial differential equation which produces the shock type traveling waves in extraordinary physical situations. Previously, this sort of equation is solved with well known tan−hyperbolic method. In this paper, we present the exact solutions of the Schamel Burgers’ equation using generalized-improved G′G and generalized G′G expansion methods with the assistance of Mathematica-12 and observe the behavior of the solutions both analytically and numerically with requisite graphs. The solutions of mentioned equation admits the shock like dynamical structures.
Topics & Concepts
Burgers' equationPartial differential equationTraveling waveMathematicsShock waveShock (circulatory)Differential equationMathematical analysisHyperbolic partial differential equationApplied mathematicsPhysicsMechanicsInternal medicineMedicineNonlinear Waves and SolitonsNonlinear Photonic SystemsFractional Differential Equations Solutions