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Generating a New Higher-Dimensional Ultra-Short Pulse System: Lie-Algebra Valued Connection and Hidden Structural Symmetries |
| Hermann T. Tchokouansi1,2**, Victor K. Kuetche1,2, Abbagari Souleymanou1,2, Thomas B. Bouetou1,2,3, Timoleon C. Kofane2 |
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, Faculty of Science, University of Yaounde I, P.O. Box 812, Cameroon
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Victor K. Kuetche, Timoleon C. Kofane, Thomas B. Bouetou et al 2012 Chin. Phys. Lett. 29 020501 |
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Abstract We carry out the hidden structural symmetries embedded within a system comprising ultra-short pulses which propagate in optical nonlinear media. Based upon the Wahlquist–Estabrook approach, we construct the Lie-algebra valued connections associated to the previous symmetries while deriving their corresponding Lax-pairs, which are particularly useful in soliton theory. In the wake of previous results, we extend the above prolongation scheme to higher-dimensional systems from which a new (2+1)-dimensional ultra-short pulse equation is unveiled along with its inverse scattering formulation, the application of which are straightforward in nonlinear optics where an additional propagating dimension deserves some attention.
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05.45.Yv
02.30.Ik
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Received: 28 July 2011
Published: 11 March 2012
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