New applications of developed Jacobi elliptic function expansion methods. (English) Zbl 1345.35091
Summary: The developed Jacobi elliptic function expansion methods are used to construct the exact periodic solutions of some non-polynomial or \((2+1)\)-dimensional nonlinear evolution equations. Some new results are presented, which include corresponding solitary or shock wave solutions and envelope solitary and shock wave solutions.
MSC:
35Q53 | KdV equations (Korteweg-de Vries equations) |
35B10 | Periodic solutions to PDEs |
35G20 | Nonlinear higher-order PDEs |
33E05 | Elliptic functions and integrals |
Keywords:
developed Jacobi elliptic function expansion methods; non-linear evolution equation; periodic solution; solitary wave solution; envelope solitary wave solutionReferences:
[1] | Wang, M. L., Phys. Lett. A, 199, 169 (1995) |
[2] | Wang, M. L.; Zhou, Y. B.; Li, Z. B., Phys. Lett. A, 216, 67 (1996) · Zbl 1125.35401 |
[3] | Yang, L.; Zhu, Z.; Yang, Y., Phys. Lett. A, 260, 55 (1999) · Zbl 0937.35016 |
[4] | Yang, L.; Liu, J.; Yang, K., Phys. Lett. A, 278, 267 (2001) · Zbl 0972.35003 |
[5] | Parkes, E. J.; Duffy, B. R., Phys. Lett. A, 229, 217 (1997) · Zbl 1043.35521 |
[6] | Fan, E., Phys. Lett. A, 277, 212 (2000) · Zbl 1167.35331 |
[7] | Hirota, R., J. Math. Phys., 14, 810 (1973) · Zbl 0261.76008 |
[8] | Kudryashov, N. A., Phys. Lett. A, 147, 287 (1990) |
[9] | Otwinowski, M.; Paul, R.; Laidlaw, W. G., Phys. Lett. A, 128, 483 (1988) |
[10] | Liu, S. K.; Fu, Z. T.; Liu, S. D.; Zhao, Q., Appl. Math. Mech., 22, 326 (2001) · Zbl 0985.35079 |
[11] | Yan, C., Phys. Lett. A, 224, 77 (1996) · Zbl 1037.35504 |
[12] | Porubov, A. V., Phys. Lett. A, 221, 391 (1996) · Zbl 0972.76546 |
[13] | Porubov, A. V.; Velarde, M. G., J. Math. Phys., 40, 884 (1999) · Zbl 0943.35087 |
[14] | Porubov, A. V.; Parker, D. F., Wave Motion, 29, 97 (1999) · Zbl 1074.35579 |
[15] | Liu, S. K.; Fu, Z. T.; Liu, S. D.; Zhao, Q., Phys. Lett. A, 289, 69 (2001) · Zbl 0972.35062 |
[16] | Fu, Z. T.; Liu, S. K.; Liu, S. D.; Zhao, Q., Phys. Lett. A, 289, 72 (2001) |
[17] | Zhang, S. Q.; Li, Z. B., Acta Phys. Sinica, 52, 1066 (2003), (in Chinese) · Zbl 1202.35060 |
[18] | Fan, E.; Zhang, J., Phys. Lett. A, 305, 383 (2002) · Zbl 1005.35063 |
[19] | Peng, Y. Z., Phys. Lett. A, 314, 401 (2003) · Zbl 1040.35102 |
[20] | Yan, Z., Chaos Solitons Fractals, 18, 299 (2003) · Zbl 1069.37060 |
[21] | Liu, S. K.; Liu, S. D., Nonlinear Equations in Physics (2000), Peking University Press: Peking University Press Beijing, (in Chinese) |
[22] | Ablowitz, M. J.; Clarkson, P. A., Soliton, Nonlinear Evolution Equations and Inverse Scattering (1991), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0762.35001 |
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.