Exact solutions for the cubic-quintic nonlinear Schrödinger equation. (English) Zbl 1154.35451
Summary: In this paper, the cubic-quintic nonlinear Schrödinger equation is solved through the extended elliptic sub-equation method. As a consequence, many types of exact travelling wave solutions are obtained which include bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35B10 | Periodic solutions to PDEs |
| 35Q51 | Soliton equations |
References:
| [1] | Angelis, C. D., IEEE J Quant Electron, 30, 818 (1994) |
| [2] | Abdullaev, F. K.; Gammal, A.; Tomio, L.; Frederico, T., Phys Rev A, 63, 043604 (2001) |
| [3] | Xhang, W.; Wright, E. M.; Pu, H.; Meystre, P., Phys Rev A, 68, 023605 (2003) |
| [4] | Inouye, S., Nature, 392, 151 (1998) |
| [5] | Sulem, C.; Sulem, P. L., The nonlinear Schrödinger equation (1999), Springer Press: Springer Press New York · Zbl 0867.35094 |
| [6] | Ablowitz, M. J.; Clarkson, P. A., Solitons, nonlinear evolution equations and inverse scattering (1991), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0762.35001 |
| [7] | Wadati, M.; Sanuki, H.; Konno, K., Prog Theor Phys, 53, 419 (1975) · Zbl 1079.35506 |
| [8] | Hirota, R., Phys Rev Lett, 27, 1192 (1971) · Zbl 1168.35423 |
| [9] | Wang, M. L., Phys Lett A, 199, 169 (1995) |
| [10] | Liu, S. K.; Fu, Z. T.; Liu, S. D.; Zhao, Q., Phys Lett A, 289, 69 (2001) · Zbl 0972.35062 |
| [11] | Yomba, E., Chaos, Solitons & Fractals, 21, 1135 (2004) · Zbl 1060.93517 |
| [12] | Fan, E. G., Chaos, Solitons & Fractals, 15, 559 (2003) · Zbl 1031.76008 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
