Fu, Zuntao; Liu, Shikuo; Liu, Shida; Zhao, Qiang New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations. (English) Zbl 0977.35094 Phys. Lett., A 290, No. 1-2, 72-76 (2001). Summary: New Jacobi elliptic functions are applied in the Jacobi elliptic function expansion method to construct the exact periodic solutions of nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this method and more shock wave solutions or solitary wave solutions can be got at their limit condition. Cited in 122 Documents MSC: 35L70 Second-order nonlinear hyperbolic equations 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 35B10 Periodic solutions to PDEs 35C10 Series solutions to PDEs Keywords:shock wave solutions; solitary wave solutions; limit condition; Jacobi elliptic function expansion method PDFBibTeX XMLCite \textit{Z. Fu} et al., Phys. Lett., A 290, No. 1--2, 72--76 (2001; Zbl 0977.35094) Full Text: DOI References: [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) [3] Yang, L.; Zhu, Z.; Wang, Y., Phys. Lett. A, 260, 55 (1999) [4] Yang, L.; Liu, J.; Yang, K., Phys. Lett. A, 278, 267 (2001) [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) [7] Hirota, R., J. Math. Phys., 14, 810 (1973) [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) [11] Yan, C., Phys. Lett. A, 224, 77 (1996) [12] Porubov, A. V., Phys. Lett. A, 221, 391 (1996) [13] Porubov, A. V.; Velarde, M. G., J. Math. Phys., 40, 884 (1999) [14] Porubov, A. V.; Parker, D. F., Wave Motion, 29, 97 (1999) [15] S.K. Liu, Z.T. Fu, S.D. Liu et al. (2001), submitted; S.K. Liu, Z.T. Fu, S.D. Liu et al. (2001), submitted [16] Bowman, F., Introduction to Elliptic Functions with Applications (1959), Universities: Universities London · Zbl 0052.07102 [17] Prasolov, V.; Solovyev, Y., Elliptic Functions and Elliptic Integrals (1997) · Zbl 0946.11001 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.