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Yao, Ruoxia; Qu, Changzheng; Li, Zhibin

Motion of curves and solutions of two multi-component mKdV equations. (English) Zbl 1069.35079

Chaos Solitons Fractals 23, No. 5, 1567-1580 (2005).
Summary: Two classes of multi-component mKdV equations have been shown to be integrable. One class called the multi-component geometric mKdV equation is exactly the system for curvatures of curves when the motion of the curves is governed by the mKdV flow. Exact solutions including solitary wave solutions of the two- and three-component mKdV equations are obtained, the symmetry reductions of the two-component geometric mKdV equation to ODE systems corresponding to it’s Lie point symmetry groups are also given. Curves and their behavior corresponding to solitary wave solutions of the two-component geometric mKdV equation are presented.

Cited in 2 Documents

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry

Keywords:

exact solutions; solitary wave solutions; symmetry reductions; Lie point symmetry
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References:

[1] Goldstein, R. E.; Petrich, D. M., Phys. Rev. Lett., 67, 3203 (1991) · Zbl 0990.37519
[2] Nakayama, K.; Segur, H.; Wadati, M., Phys. Rev. Lett., 69, 2603 (1992) · Zbl 0968.53500
[3] Nakayama, K.; Wadati, M., J. Phys. Soc. Jpn., 62, 473 (1993) · Zbl 0972.53501
[4] Langer, J.; Perline, R., Phys. Lett. A, 239, 36 (1998) · Zbl 0940.53002
[5] Sokolov, V. V.; Wolf, T., J. Phys. A Math. Gen., 34, 11139 (2001) · Zbl 0988.35159
[6] Wang, J. P., Generalized Hasimoto transformation and vector sine-Gordon equation. SPT 2002: symmetry and perturbation theory (Cala Gonone) (2002), World Scientific Publishing: World Scientific Publishing River Edge, NJ, p. 276-83
[7] Tsuchida, T.; Wadati, M., J. Phys. Soc. Jpn., 67, 1175 (1998) · Zbl 0973.35170
[8] Qu CZ, Yao RX, Liu RC, In press; Qu CZ, Yao RX, Liu RC, In press
[9] Wadati, M.; Konno, K.; Ichikawa, Y., J. Phys. Soc. Jpn., 47, 1998 (1979)
[10] Ichikawa, Y.; Konno, K.; Wadati, M., J. Phys. Soc. Jpn., 50, 1799 (1981)
[11] Wadati, M.; Konno, K.; Ichikawa, Y., J. Phys. Soc. Jpn., 46, 1965 (1979) · Zbl 1334.81106
[12] Hasimoto, H., J. Fluid Mech., 51, 477 (1972) · Zbl 0237.76010
[13] Lamb, G. L., J. Math. Phys., 8, 1654 (1977)
[14] Lakshmanan, M., J. Math. Phys., 20, 1667 (1979) · Zbl 0416.70016
[15] Schief, W. K.; Rogers, C., Proc. R. Soc. London A, 455, 3163 (1999) · Zbl 0981.53061
[16] Doliwa, A.; Santini, P. M., Phys. Lett. A, 85, 373 (1994) · Zbl 0941.37532
[17] Nakayama, K., J. Phys. Soc Jpn., 67, 3031 (1998) · Zbl 0947.53002
[18] Nakayama, K., J. Phys. Soc. Jpn., 68, 3214 (1999) · Zbl 0979.53005
[19] Chou, K. S.; Qu, C. Z., J. Phys. Soc. Jpn., 70, 1912 (2001) · Zbl 1058.37052
[20] Chou, K. S.; Qu, C. Z., Physica D, 162, 9 (2002) · Zbl 0987.35139
[21] Chou, K. S.; Qu, C. Z., Chaos, Solitons, & Fractals, 14, 29 (2002) · Zbl 1014.37047
[22] Chou, K. S.; Qu, C. Z., J. Nonlinear Sci., 13, 487 (2003) · Zbl 1045.35063
[23] Qu, C. Z.; Si, Y. Q.; Liu, R. C., Chaos, Solitons, & Fractals, 15, 131 (2003) · Zbl 1038.35099
[24] Qu, C. Z.; Zhang, S. L.; Zhang, Q. J., Z. Naturforsch., 58, 75 (2003)
[25] Qu, C. Z., Commum. Theor. Phys., 39, 401 (2003)
[26] Chou, K. S.; Qu, C. Z., Chaos, Solitons, & Fractals, 19, 47 (2004) · Zbl 1069.37057
[27] Sasaki, R., Nucl. Phys. B, 154, 343 (1979)
[28] Chern, S. S.; Peng, C. K., Manuscri. Math., 28, 207 (1979) · Zbl 0408.35074
[29] Chern, S. S.; Tenenblat, K., Stud. Appl. Math., 74, 55 (1986) · Zbl 0605.35080
[30] Rabelo, M. L., Stud. Appl. Math., 81, 221 (1989) · Zbl 0696.35111
[31] Kamran, N.; Tenenblat, K., J. Diff. Equat., 115, 75 (1995) · Zbl 0815.35036
[32] Reyes, E. G., J. Diff. Equat, 153, 223 (1999)
[33] Yao, R. X.; Li, Z. B., Phys. Lett. A, 297, 196 (2002) · Zbl 0995.35003
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.