*(English)*Zbl 1092.35524

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), $\sqrt{1+\text{sgn}\left(b\right){w}^{2}}$ should be changed to $\sqrt{\text{sgn}\left(b\right)(b+{w}^{2})}$.

##### MSC:

35Q53 | KdV-like (Korteweg-de Vries) equations |

35B40 | Asymptotic behavior of solutions of PDE |

35Q51 | Soliton-like equations |

37K10 | Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies |