×

On the continuous limits and integrability of a new coupled semidiscrete mKdV system. (English) Zbl 1316.35258

Summary: In this paper, we aim to get more insight on the relation between semidiscrete coupled mKdV system (where “semidiscrete” means that the system is discrete in the space variable and continuous in time) and the coupled mKdV equations; to this purpose, we propose a new coupled semidiscrete mKdV system. The Lax pairs, the Darboux transformation, soliton solutions and conservation laws for the coupled semidiscrete mKdV system are given. The coupled mKdV theory including the Lax pairs, the Darboux transformation, soliton solutions, and conservation laws is recovered through the continuous limits of corresponding theory for the new semidiscrete mKdV system.{
©2011 American Institute of Physics}

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
39A12 Discrete version of topics in analysis
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35C08 Soliton solutions
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Schwarz, M., Adv. Math., 44, 132 (1982) · Zbl 0508.58025 · doi:10.1016/0001-8708(82)90003-2
[2] Kupershmidt, B. A., Discrete Lax equations and differential-difference calculus (1985) · Zbl 0565.58024
[3] Zeng, Y.; Wojciechowski, S. R., J. Phys. A, 28, 3825 (1995) · Zbl 0859.35114 · doi:10.1088/0305-4470/28/13/026
[4] Morosi, C.; Pizzocchero, L., Commun. Math. Phys., 180, 505 (1996) · Zbl 0873.35085 · doi:10.1007/BF02099723
[5] Gieseker, D., Commun. Math. Phys., 181, 587 (1996) · Zbl 0867.35096 · doi:10.1007/BF02101288
[6] Gear, J. A., Stud. Appl. Math., 72, 95 (1985) · Zbl 0561.76030
[7] Brazhnyi, V. A.; Konotop, V. V., Phys. Rev. E, 72, 026616 (2005) · doi:10.1103/PhysRevE.72.026616
[8] Lou, S. Y.; Tong, B.; Hu, H. C.; Tang, X. Y., J. Phys. A: Math. Gen., 39, 513 (2006) · Zbl 1082.76023 · doi:10.1088/0305-4470/39/3/005
[9] Lou, S. Y.; Tong, B.; Ja, M.; Li, J. H., A coupled Volterra system and its exact solutions (2007)
[10] Zhao, H. Q.; Zhu, Z. N., J. Math. Phys., 52, 023512 (2011) · Zbl 1314.35156 · doi:10.1063/1.3549121
[11] Iwao, M.; Hirota, R., J. Phys. Soc. Jpn., 66, 577 (1997) · Zbl 0946.35078 · doi:10.1143/JPSJ.66.577
[12] Tsuchida, T.; Wadati, M., J. Phys. Soc. Jpn., 67, 1175 (1998) · Zbl 0973.35170 · doi:10.1143/JPSJ.67.1175
[13] Svinolupov, S. I., Commun. Math. Phys., 143, 559 (1992) · Zbl 0753.35100 · doi:10.1007/BF02099265
[14] Tsuchida, T.; Ujino, J. H.; Wadati, M., J. Math. Phys., 39, 4785 (1998) · Zbl 0933.35176 · doi:10.1063/1.532537
[15] Gordoa, P. R.; Pickering, A.; Zhu, Z. N., J. Math. Phys., 51, 053505 (2010) · Zbl 1310.37032 · doi:10.1063/1.3397483
[16] Zhang, H. Q.; Tian, B.; Xu, T.; Li, H.; Zhang, C.; Zhang, H., J. Phys. A: Math. Theor., 41, 355210 (2008) · Zbl 1144.82007 · doi:10.1088/1751-8113/41/35/355210
[17] Adler, V. E.; Postnikov, V. V., J. Phys. A: Math. Theor., 41, 455203 (2008) · Zbl 1157.35464 · doi:10.1088/1751-8113/41/45/455203
[18] Suris, Y. B., Phys. Lett. A, 234, 91 (1997) · Zbl 1044.35523 · doi:10.1016/S0375-9601(97)00592-6
[19] Gordoa, P. R.; Pickering, A.; Zhu, Z. N., Chaos, Solitons and Fractals, 29, 862 (2006) · Zbl 1142.37369 · doi:10.1016/j.chaos.2005.08.060
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.