The Variable Separation Method and Exact Jacobi Elliptic Function Solutions for the Nizhnik-Novikov-Veselov Equation

Peng, Y.

doi:10.12693/APhysPolA.110.3

Journal

Acta Physica Polonica A

2006 | 110 | 1 | 3-9

Article title

The Variable Separation Method and Exact Jacobi Elliptic Function Solutions for the Nizhnik-Novikov-Veselov Equation

Authors

Y. Peng

Content

Full texts:

http://przyrbwn.icm.edu.pl/APP/PDF/110/a110z101.pdf [remote]

Title variants

Languages of publication

Abstracts

Based on the singular structure analysis, the variable separation method is proposed for the Nizhnik-Novikov-Veselov equation to obtain a general functional separation solution containing three arbitrary functions. Choosing these arbitrary functions to be the Jacobi elliptic functions, a diversity of elliptic function solutions may be obtained for the equation of interest. The interaction property of the waves is numerically studied. The long wave limit gives the new type of localized coherent structures.

Keywords

02.30.Jr

Discipline

02.30.Jr: Partial differential equations

Publisher

Journal

Acta Physica Polonica A

Year

2006

Volume

110

Issue

Pages

3-9

Physical description

Dates

published

2006-07

received

2005-10-10

(unknown)

2006-01-31

Contributors

author

Y. Peng

Department of Mathematics, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China

References

1. W. Miller, Jr., in: Symmetries and Nonlinear Phenomena, Eds. D. Levi, P. Winternitz, World Scientific, London 1989, p. 188
2. Y.-Z. Peng, Acta Phys. Pol. A, 103, 417, 2003; 105, 417, 2004; 108, 421, 2005
3. E.G. Kalnins, W. Miller, J. Math. Phys., 26, 1560, 1985
4. O.V. Kaptsov, Nonlinear Anal., 19, 753, 1992
5. W. Miller, Jr., L.A. Rubel, J. Phys. A, 26, 1901, 1992
6. R.Z. Zhdanov, J. Phys. A, 27, L291, 1994
7. E. Pucci, G. Saccomandi, Physica D, 139, 28, 2000
8. C.Z. Qu, S.L. Zhang, R.C. Liu, Physica D, 144, 97, 2000
9. L.P. Nizhnik, Sov. Phys. Dokl., 25, 706, 1980
10. S.P. Novikov, A.P. Veselov, Physica D, 18, 267, 1986
11. M. Boiti, P.J. Leon, M. Manna, F. Pempinelli, Inverse Problems, 2, 271, 1986
12. R. Radha, M. Lakshmanan, J. Math. Phys., 35, 4746, 1994
13. R. Conte, Lect. Notes Phys., 632, 1, 2003
14. H.C. Hu, S.Y. Lou, Q.P. Liu, arXiv: nlin. SI/0210012 v1 7 Oct 2002
15. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions, Dover, New York 1972

Document Type

Publication order reference

Identifiers

DOI

10.12693/APhysPolA.110.3

YADDA identifier

bwmeta1.element.bwnjournal-article-appv110n101kz