Fu, Zuntao; Liu, Shikuo; Liu, Shida Multiple structures of two-dimensional nonlinear Rossby wave. (English) Zbl 1067.35071 Chaos Solitons Fractals 24, No. 1, 383-390 (2005). Summary: The elliptic equation is taken as a transformation and applied to solve the Zakharov-Kuznetsov equation, which has been derived by Gottwald as a two-dimensional model for nonlinear Rossby waves. It is shown that more kinds of solutions are derived, such as periodic solutions of rational form, periodic solutions and so on. Cited in 9 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76B65 Rossby waves (MSC2010) 37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions 35C05 Solutions to PDEs in closed form Keywords:Zakharov-Kuznetsov equation; periodic solutions PDF BibTeX XML Cite \textit{Z. Fu} et al., Chaos Solitons Fractals 24, No. 1, 383--390 (2005; Zbl 1067.35071) Full Text: DOI OpenURL References: [1] Gottwalld GA, The Zakharov-Kuznetsov equation as a two-dimenional model for nonlinear Rossby wave. arXiv: nlin, 0312009; 2003 [2] Iwasaki, H.; Toh, S.; Kawahara, T., Phys. D, 43, 293, (1990) [3] Fu, Z.T.; Liu, S.D.; Liu, S.K., Commun. theor. phys., 39, 5, 531, (2003) [4] Fu, Z.T.; Liu, S.K.; Liu, S.D., Commun. theor. phys., 40, 3, 285, (2003) [5] Fu, Z.T.; Chen, Z.; Liu, S.K.; Liu, S.D., Commun. theor. phys., 41, 5, 675, (2004) [6] Fu, Z.T.; Liu, S.D.; Liu, S.K.; Chen, Z., Chaos, solitons & fractals, 22, 2, 335, (2004) [7] Liu, S.K.; Liu, S.D., Nonlinear equations in physics, (2000), Peking University Press Beijing [8] Fan, E.G., Phys. lett. A, 277, 212, (2000) [9] Yan, Z.Y.; Zhang, H.Q., Phys. lett. A, 285, 355, (2001) [10] Bowman, F., Introduction to elliptic functions with applications, (1959), Universities London · Zbl 0052.07102 [11] Prasolov, V.; Solovyev, Y., Elliptic functions and elliptic integrals, (1997), American Mathematical Society Providence R.I. · Zbl 0946.11001 [12] Wang, Z.X.; Guo, D.R., Special functions, (1989), World Scientific Publishing Singapore · Zbl 0724.33001 [13] Clarkson, P.A.; Mansfield, E.L., Phys. D, 70, 250, (1993) [14] Coleman, C.J., J. aust. math. soc. ser. B, 33, 1, (1992) [15] Kudryashov, N.A.; Zargaryan, D., J. phys. A, 29, 8067, (1996) [16] Smyth, N.F., J. aust. math. soc. ser. B, 33, 403, (1992) [17] Yan, C.T., Phys. lett. A, 224, 77, (1996) [18] Wang, M.L., Phys. lett. A, 199, 169, (1995) [19] Parkes, E.J.; Duffy, B.R., Phys. lett. A, 229, 217, (1997) · Zbl 1043.35521 [20] Fu, Z.T.; Liu, S.K.; Liu, S.D.; Zhao, Q., Phys. lett. A, 290, 72, (2001) [21] Liu, S.K.; Fu, Z.T.; Liu, S.D.; Zhao, Q., Phys. lett. A, 289, 69, (2001) [22] Hirota, R., J. math. phys., 14, 810, (1973) [23] Kudryashov, N.A., Phys. lett. A, 147, 287, (1990) [24] Fu, Z.T.; Liu, S.K.; Liu, S.D., Phys. lett. A, 299, 507, (2002) [25] Liu, S.K.; Fu, Z.T.; Liu, S.D.; Zhao, Q., Appl. math. mech., 22, 326, (2001) [26] Otwinowski, M.; Paul, R.; Laidlaw, W.G., Phys. lett. A, 128, 483, (1988) 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.