×

Duffing’s equation and its applications to the Hirota equation. (English) Zbl 1056.35140

Summary: In this letter, we illustrate a connection between the Duffing’s equation and the Hirota equation. By applying the exact solutions of the Duffing’s equation, we obtain two periodic wave solutions in terms of Jacobi elliptic functions to the Hirota equation.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Hirota, R., J. Math. Phys., 14, 805 (1973)
[2] Zaakharov, V. E.; Shabat, A. B., Sov. Phys. JEPT, 34, 62 (1972)
[3] Miura, R. M., J. Math. Phys., 9, 1202 (1968)
[4] Maccari, A., J. Math. Phys., 39, 6547 (1998)
[5] Fan, E.; Zhang, J., Phys. Lett. A, 305, 383 (2002)
[6] Feng, Z.; Ji, W.; Fei, S., Math. Practice Theory, 27, 222 (1997)
[7] Hale, J. K., Ordinary Differential Equations (1980), John Wiley & Sons: John Wiley & Sons New York · Zbl 0186.40901
[8] Feng, Z., Phys. Lett. A, 302, 64 (2002)
[9] Bogolubsky, I. L., Comput. Phys. Commun., 13, 149 (1977)
[10] Clarkson, P. A., Stud. Appl. Math., 75, 95 (1986)
[11] Kundu, A., J. Math. Phys., 25, 3433 (1984)
[12] Feng, Z., Phys. Lett. A, 293, 50 (2002)
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.