Some new exact traveling wave solutions to the simplified MCH equation and the (1 + 1)-dimensional combined KdV–mKdV equations

The generalized (G′/G)-expansion method is thriving in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. In this paper, we bring to bear the generalized (G′/G)-expansion method to look for the exact solutions via the simplified MCH equation and the (1 + 1)-dimensional combined KdV–mKdV equations involving parameters. When the parameters take special values, solitary wave solutions are originated from the traveling wave solutions. It is established that the generalized (G′/G)-expansion method offers a further influential mathematical tool for constructing the exact solutions of NLEEs in mathematical physics.