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Conservation laws of a perturbed Kaup–Newell equation

Jing-Yun Yang

School of Mathematical and Physical Sciences, Xuzhou Institute of Technology, Xuzhou 221111, Jiangsu, China

E-mail Address: 1398025989@qq.com

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and

Wen-Xiu Ma

Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA

E-mail Address: mawx@cas.usf.edu

Corresponding authors.

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https://doi.org/10.1142/S0217984916503814Cited by:24 (Source: Crossref)

Abstract

A new Lax pair is introduced for a perturbed Kaup–Newell equation and used to construct two series of conservation laws through a Riccati equation that a ratio of eigenfunctions satisfies. Both series of conservation laws are defined recursively, and the first two in each series are presented explicitly.

Keywords:

PACS: 02.30.Ik

References

1. F. Magri, J. Math. Phys. 19 (1978) 1156. Crossref, Web of Science, ADS, Google Scholar
2. W. X. Ma and M. Chen, J. Phys. A: Math. Gen. 39 (2006) 10787. Crossref, ADS, Google Scholar
3. W. X. Ma, J. Phys. A: Math. Gen. 40 (2007) 15055. Crossref, ADS, Google Scholar
4. S. C. Anco and G. Bluman, Phys. Rev. Lett. 78 (1997) 2869. Crossref, Web of Science, ADS, Google Scholar
5. N. H. Ibragimov, J. Math. Anal. Appl. 333 (2007) 311. Crossref, Web of Science, Google Scholar
6. W. X. Ma, Symmetry 7 (2015) 714. Crossref, Web of Science, ADS, Google Scholar
7. M. Wadati, Stud. Appl. Math. 59 (1978) 153. Crossref, Web of Science, Google Scholar
8. J. M. Alberty, T. Koikawa and R. Sasaki, Physica D 5 (1982) 43. Crossref, Web of Science, ADS, Google Scholar
9. Y. Q. Yao and W. X. Ma, preprint (2015). Google Scholar
10. D. J. Kaup and A. C. Newell, J. Math. Phys. 19 (1978) 798. Crossref, Web of Science, ADS, Google Scholar
11. W. X. Ma and R. G. Zhou, J. Phys. A: Math. Gen. 32 (1999) L239. Crossref, ADS, Google Scholar
12. P. Guha, Rep. Math. Phys. 50 (2002) 1. Crossref, Web of Science, ADS, Google Scholar
13. Y. P. Zhang, J. Liu and G. G. Wei, Appl. Math. Lett. 45 (2015) 58. Crossref, Web of Science, Google Scholar
14. L. Liu, B. Tian, W. R. Sun, Y. F. Wang and Y. P. Wang, Mod. Phys. Lett. B 30 (2016) 1650008. Link, Web of Science, ADS, Google Scholar
15. W. X. Ma, Q. Ding, W. G. Zhang and B. Q. Lu, Nuovo Cimento B 111 (1996) 1135. Crossref, Web of Science, ADS, Google Scholar
16. F. Gesztesy and R. Ratnaseelan, Rev. Math. Phys. 10 (1998) 345. Link, Web of Science, ADS, Google Scholar
17. X. G. Geng and C. W. Cao, Phys. Lett. A 261 (1999) 289. Crossref, Web of Science, ADS, Google Scholar
18. W. X. Ma, arXiv:1607.07532. Google Scholar
19. Y. Zhang and W. X. Ma, Appl. Math. Comput. 256 (2015) 252. Crossref, Web of Science, Google Scholar
20. W. X. Ma, Phys. Lett. A 379 (2015) 1975. Crossref, Web of Science, ADS, Google Scholar
21. X. Lü, W. X. Ma, S. T. Chen and C. M. Khalique, Appl. Math. Lett. 58 (2016) 13. Crossref, Web of Science, Google Scholar
22. W. X. Ma, Z. Y. Qin and X. Lü, Nonlinear Dynam. 84 (2016) 923. Crossref, Web of Science, Google Scholar
23. R. Hirota, The Direct Method in Soliton Theory (Cambridge University Press, Cambridge, 2004). Crossref, Google Scholar
24. W. X. Ma, Stud. Nonlinear Sci. 2 (2011) 140. Google Scholar
25. W. X. Ma, J. Phys.: Conf. Ser. 411 (2013) 012021. Crossref, ADS, Google Scholar
26. W. X. Ma, Rep. Math. Phys. 72 (2013) 41. Crossref, Web of Science, ADS, Google Scholar