Travelling wave solutions of reduced super-KdV equation: A perspective from Lamé equation. (English) Zbl 1197.35251
Summary: Reduced supersymmetric Korteweg-de Vries (super-KdV) equation is investigated in this paper, with the help of an auxiliary Lamé equation and Jacobi elliptic function, travelling wave solutions of reduced super-KdV equation are obtained in the form of Jacobi elliptic periodic function, meanwhile, trigonal solutions and hyperbolic solutions are derived.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35C07 | Traveling wave solutions |
| 35C09 | Trigonometric solutions to PDEs |
| 35A24 | Methods of ordinary differential equations applied to PDEs |
Keywords:
super-KdV equation; Lamé equation; Jacobi elliptic function; trigonal solutions; hyperbolic solutionsReferences:
| [1] | Zhang, D., Integrability of the \(N=3\) super KdV equation, J. Phys. A: Math. Gen., 29, 8163-8167 (1996) · Zbl 0906.35094 |
| [2] | Hong, B., New Jacobi elliptic functions solutions for the variable-coefficient mKdV equation, Appl. Math. Comput., 215, 2908-2913 (2009) · Zbl 1180.35459 |
| [3] | Zhu, Z. N., Soliton-like solutions of generalized KdV equation with external force term, Acta Phys. Sin., 41, 1561-1566 (1992) · Zbl 0810.35118 |
| [4] | Chan, W. L.; Zhang, X., Symmetries, conservation laws and Hamiltonian structures of the non-isospectral and variable coefficient KdV and MKdV equations, J. Phys. A: Math. Gen., 28, 407-412 (1995) · Zbl 0853.35105 |
| [5] | Xiang, C., Analytical solutions of KdV equation with relaxation effect of inhomogeneous medium, Appl. Math. Comput., 216, 2235-2239 (2010) · Zbl 1192.35158 |
| [6] | Kulish, Petr P.; Zeitlin, Anton M., Super-KdV equation: classical solutions and quantization, PAMM Proc. Appl. Math. Mech., 4, 576-577 (2004) · Zbl 1354.35130 |
| [7] | Kulish, Petr P.; Zeitlin, Anton M., Integrable structure of superconformal field theory and quantum super-KdV theory, Phys. Lett. B, 581, 125-132 (2004) · Zbl 1246.81074 |
| [8] | McArthur, I. N., On the integrability of the super-KdV equation, Commun. Math. Phys., 148, 177-188 (1992) · Zbl 0753.35086 |
| [9] | Kersten, P. H.M.; Gragert, P. K.H., Symmetries for the super-KdV equation, J. Phys. A: Math. Gen., 21, L579-L584 (1988) · Zbl 0662.35113 |
| [10] | Fu, Z.; Yuan, N.; Mao, J.; Liu, S., Multi-order exact solutions to the Drinfeld-Sokolov-Wilson equations, Phys. Lett. A, 373, 3710-3714 (2009) · Zbl 1233.83002 |
| [11] | Liu, G.-T., Lame equation and asymptotic higher-order periodic solutions to nonlinear evolution equations, Appl. Math. Comput., 212, 312-317 (2009) · Zbl 1177.34073 |
| [12] | Fu, Z. T.; Liu, S. K.; Liu, S. D.; Zhao, Q., New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations, Phys. Lett. A, 290, 72-76 (2001) · Zbl 0977.35094 |
| [13] | Salur, Sema, Deformations of special Lagrangian submanifolds; an approach via Fredholm alternative, Gokova Geom-Top., 1, 154-161 (2006) · Zbl 1101.53051 |
| [14] | Brezis, Haim; Browder, Felix, Partial differential equations in the 20th century, Adv. Math., 135, 76-144 (1998) · Zbl 0915.01011 |
| [15] | Zimmerman, W. B.; Rees, J. M., Long solitary internal waves in stable stratifications, Nonlinear Process. Geophys., 11, 165-180 (2004) |
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