NEW EXTENDED (G′/G)-EXPANSION METHOD FOR TRAVELING WAVE SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS (NPDEs) IN MATHEMATICAL PHYSICS

Abstract

The new extended (G′/G)-expansion method is proposed to construct abundant exact traveling wave solutions involving free parameters to the nonlinear partial differential equations (NPDEs) in mathematical physics.  We highlight the power of the new extended (G′/G)-expansion method in providing generalized solitary wave solutions of different physical structures applying it in the right-handed noncommutative burgers and the (1+1)-dimensional compound KdVB equations.  By this application, we enhanced new traveling wave solutions of the equations which can be used to exploit some practical physical and mechanical phenomena.  Moreover, when the parameters are replaced by special values, the well-known solitary wave solutions of the equation rediscovered from the traveling waves that may imply some physical meaningful results in fluid mechanics, gas dynamics, traffic flow, nonlinear dispersion and dissipation effects.