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Prolongation Structure Analysis of a Coupled Dispersionless System |
| Souleymanou Abbagari1,2**, Bouetou Bouetou Thomas1,2, Kuetche Kamgang Victor1,2, Mouna Ferdinand3,4, Timoleon Crepin Kofane2
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1National Advanced School of Engineering, University of Yaounde I, P.O. Box. 8390, Cameroon
2Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box. 812, Cameroon
3Department of Mathematics, Higher Teacher's Training College, University of Maroua, P.O. Box. 46, Cameroon
4Department of Mathematics, Faculty of Science, University of Yaounde I, P.O. Box 812, Cameroon
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Souleymanou Abbagari, Bouetou Bouetou Thomas, Kuetche Kamgang Victor et al 2011 Chin. Phys. Lett. 28 020204 |
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Abstract We address the problem of integrability of a coupled dispersionless system recently introduced by Zhaqilao, Zhao and Li [Chin. Phys. B 18 (2009) 1780] which physically describes the propagation of electromagnetic fields within an optical nonlinear medium, but also arrives in the physical description of a charged object dynamics in an external magnetic field. Following the prolongation structure analysis developed by Wahlquist and Estabrook, we derive a more general form of Lax pairs of the previous coupled dispersionless system and its concrete non-Abelian Lie algebra resorting to a hidden symmetry. Also, we construct the Bäcklund transformation of the system using the Riccati form of the linear eigenvalue problem.
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02.03.Ik
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Received: 17 June 2010
Published: 30 January 2011
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