A note on loop-soliton solutions of the short-pulse equation. (English) Zbl 1238.35119
Summary: It is shown that the \(N\)-loop soliton solution to the short-pulse equation may be decomposed exactly into \(N\) separate soliton elements by using a Moloney-Hodnett type decomposition. For the case \(N=2\), the decomposition is used to calculate the phase shift of each soliton caused by its interaction with the other one. Corrections are made to some previous results in the literature [V. K. Kuetche, T. B. Bouetou and T. C. Kofane, Phys. Lett., A 372, No. 29, 4891-4897 (2008; Zbl 1221.58025); A. Sakovich and S. Sakovich, J. Phys. A, Math. Gen. 39, No. 22, L361-L367 (2006; Zbl 1092.81531)].
Keywords:
short-pulse equation; sine-Gordon equation; \(N\)-loop soliton; Moloney-Hodnett decomposition; phase shiftReferences:
| [1] | Schäfer, T.; Wayne, C. E., Physica D, 196, 90 (2004) · Zbl 1054.81554 |
| [2] | Sakovich, A.; Sakovich, S., SIGMA, 3, 086 (2007) · Zbl 1136.35094 |
| [3] | Shen, Y.; Williams, F.; Whitaker, N.; Kevrekidis, P. G.; Saxena, A.; Frantzeskakis, D. J., Phys. Lett. A, 374, 2964 (2010) · Zbl 1248.35198 |
| [4] | Kuetche, V. K.; Bouetou, T. B.; Kofane, T. C., J. Phys. Soc. Jpn., 76, 024004 (2007) |
| [5] | Kuetche, V. K.; Bouetou, T. B.; Kofane, T. C., Phys. Lett. A, 372, 665 (2008) · Zbl 1217.74063 |
| [6] | Sakovich, A.; Sakovich, S., J. Phys. A Math. Gen., 39, L361 (2006) · Zbl 1092.81531 |
| [7] | Matsuno, Y., J. Phys. Soc. Jpn., 76, 084003 (2007) |
| [8] | Kakuhata, H.; Konno, K., J. Phys. Soc. Jpn., 68, 757 (1999) · Zbl 0944.81025 |
| [9] | Fu, Z.; Chen, Z.; Zhang, L.; Mao, J.; Liu, S., Appl. Math. Comput., 215, 3899 (2010) · Zbl 1185.35224 |
| [10] | Sakovich, A.; Sakovich, S., J. Phys. Soc. Jpn., 74, 239 (2005) · Zbl 1067.35115 |
| [11] | Matsuno, Y., J. Math. Phys., 49, 073508 (2008) · Zbl 1152.81554 |
| [12] | Parkes, E. J., Chaos Solitons Fractals, 38, 154 (2008) · Zbl 1142.35575 |
| [13] | Hirota, R., J. Phys. Soc. Jpn., 33, 1459 (1972) |
| [14] | Hirota, R., Prog. Theor. Phys., 52, 1498 (1974) · Zbl 1168.37322 |
| [15] | Hirota, R.; Satsuma, J., Prog. Theor. Phys. Suppl., 59, 64 (1976) |
| [16] | Hirota, R., The Direct Method in Soliton Theory (2004), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1099.35111 |
| [17] | Moloney, T. P.; Hodnett, P. F., Proc. R. Irish Acad. A, 89, 205 (1989) · Zbl 0678.35088 |
| [18] | Vakhnenko, V. O.; Parkes, E. J., Nonlinearity, 11, 1457 (1998) · Zbl 0914.35115 |
| [19] | Morrison, A. J.; Parkes, E. J.; Vakhnenko, V. O., Nonlinearity, 12, 1427 (1999) · Zbl 0935.35129 |
| [20] | Lamb, G. L., Elements of Soliton Theory (1980), Wiley: Wiley New York · Zbl 0445.35001 |
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.
