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Zbl 1092.35524
Yan, Zhenya
New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations. (English)
[J] Phys. Lett., A 292, No. 1-2, 100-106 (2001), erratum 298, No. 2-3, 211 (2002). ISSN 0375-9601

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 {\it 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 $$u(\xi)=\sum_{i=1}^mw^{i-1}\left[A_iw+B_i\sqrt{\text{sgn}(b) (b+w^2)}\right]+A_0+\sum_{j=0}^nD_j\xi^j.$$ On page 104, there are two misprints in equation (21), which should be changed to $$\cases u=A_0+A_1w+B_1\sqrt{\text{sgn}(b)(b+w^2)},\\ v=a_0+a_1w+b_1\sqrt{\text{sgn}(b)(b+w^2)}.\endcases$$ In the paragraph under equation (21), $\sqrt{1+\text{sgn}(b)w^2}$ should be changed to $\sqrt{\text{sgn}(b)(b+w^2)}$.

MSC 2000:: *35Q53 KdV-like equations
35B40 Asymptotic behavior of solutions of PDE
35Q51 Solitons
37K10 Completely integrable systems etc.

Keywords: Coupled potential KdV equation; Modified KdV-type equation; Riccati equation; Symbolic computation; Exact solution

Citations: Zbl 0987.37064

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