Summary: In this Letter, a more powerful method to seek exact travelling wave solutions of nonlinear partial differential equations is presented, which uses the good ideas of the extended-tanh function method and our previous method. The two new integrable coupled potential KdV equation and modified KdV-type equations which were firstly presented by M. V. Foursov [J. Math. Phys. 41, No. 9, 6173–6185 (2000; Zbl 0987.37064)] are chosen to illustrate the method by using symbolic computation such that multiple travelling wave solutions are obtained which contain new kink-like soliton solutions, kink-shaped solitons, bell-shaped solitons, rational solutions and singular solitons that may be useful to explain the “blow-up” phenomena.
Summary of the erratum: On page 101, there is a misprint in equation (9), which should be changed to
On page 104, there are two misprints in equation (21), which should be changed to
In the paragraph under equation (21), should be changed to .