The generalizing Riccati equation mapping method in non-linear evolution equation: Application to \((2 + 1)\)-dimensional Boiti-Leon-Pempinelle equation. (English) Zbl 1142.35597
Summary: The tanh method is used to find travelling wave solutions to various wave equations. In this paper, the extended tanh function method is further improved by the generalizing Riccati equation mapping method and picking up its new solutions. In order to test the validity of this approach, the \((2 + 1)\)-dimensional Boiti-Leon-Pempinelle equation is considered. As a result, the abundant new non-travelling wave solutions are obtained.
References:
| [1] | Ablowitz, M. J.; Clarkson, P. A., Soliton, nonlinear evolution equations and inverse scattering (1991), Cambridge University Press: Cambridge University Press New York · Zbl 0762.35001 |
| [2] | Gardner, C. S.; Greene, J. M.; Kruskal, M. D., Phys Rev Lett, 19, 1095 (1967) · Zbl 1103.35360 |
| [3] | Wadati, M., J Phys Soc Jpn I, 38, 673 (1975) · Zbl 1334.82022 |
| [4] | Wadati, M., J Phys Soc Jpn II, 38, 681 (1975) · Zbl 1334.82023 |
| [5] | Conte, R.; Musette, M., J Phys A: Math Gen, 25, 5609 (1992) · Zbl 0782.35065 |
| [6] | Hirota, R.; Satsuma, J., Phys Lett A, 85, 407 (1981) |
| [7] | Xie, F. D., Chaos, Solitons & Fractals, 20, 1005 (2004) · Zbl 1049.35164 |
| [8] | Gao, Y. T.; Tian, B., Comput Math Appl, 30, 97 (1995) · Zbl 0836.35140 |
| [9] | Parkes, E. J., Comput Phys Commun, 98, 288 (1996) |
| [10] | Fan, E. G., Phys Lett A, 277, 212 (2000) · Zbl 1167.35331 |
| [11] | Yan, Z. Y., Phys Lett A, 292, 100 (2001) |
| [12] | Li, B.; Chen, Y.; Zhang, H. Q., Chaos, Solitons & Fractals, 15, 647 (2003) · Zbl 1038.35095 |
| [13] | Elwakil, S. A., Appl Math Comput, 161, 403 (2005) · Zbl 1062.35082 |
| [14] | Lü, Z. S.; Zhang, H. G., Chaos, Solitons & Fractals, 17, 669 (2003) · Zbl 1030.35140 |
| [15] | Boiti, M.; Leon, J. P.; Pempinelle, F., Invers Problem, 3, 37 (1987) · Zbl 0625.35073 |
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