Generating a New Higher-Dimensional Coupled Integrable Dispersionless System: Algebraic Structures,Bäcklund Transformation and Hidden Structural Symmetries |
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Authors: | Souleymanou Abbagari Thomas B Bouetou Timoleon C Kofane |
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Institution: | 1. National Advanced School of Engineering, University of Yaounde I, P.O. Box 8390, Cameroon;
2. Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Cameroon;
3. The Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany |
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Abstract: | The prolongation structure methodologies of Wahlquist-Estabrook H.D. Wahlquist and F.B. Estabrook, {J. Math. Phys.} 16 (1975) 1] for nonlinear differential equations are applied to a more general set of coupled integrable dispersionless system. Based on the obtained prolongation structure, a Lie-Algebra valued connection of a closed ideal of exterior differential forms related to the above system is constructed. A Lie-Algebra representation of some hidden structural symmetries of the previous system, its Bäcklund transformation using the Riccati form of the linear eigenvalue problem and their general corresponding Lax-representation are derived. In the wake of the previous results, we extend the above prolongation scheme to higher-dimensional systems from which a new (2+1)-dimensional coupled integrable dispersionless system is unveiled along with its inverse scattering formulation, which applications are straightforward in nonlinear optics where additional propagating dimension deserves some attention. |
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Keywords: | coupled integrable dispersionless system algebraic structures Bäcklund transformation Hidden structural symmetries |
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