On symmetries,reductions, conservation laws and conserved quantities of optical solitons with inter-modal dispersion |
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Authors: | R Morris P Masemola AH Kara Anjan Biswas |
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Institution: | 1. School of Mathematics and Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Johannesburg, Wits 2050, South Africa;2. Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA;3. Department of Mathematics Faculty of Science, Jeddah, Saudi Arabia |
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Abstract: | This paper studies the compressional dispersive Alfvén (CDA) waves where Noether symmetries will be calculated from which the corresponding conservation laws will be obtained via Noether's theorem. Furthermore, one case of double reduction is performed via the association of a conserved vector with a Noether symmetry (with zero gauge). The conserved quantities of optical solitons in the presence of intermodal dispersion that is governed by the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity. The invariance-multiplier method is adopted to carry out the analysis, from which the conserved densities are then retrieved. Finally, the conserved quantities are obtained using the 1-soliton solution of the governing equation. |
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Keywords: | Wave equation Nonlinear Schrö dinger equation Symmetries Multipliers Conservation laws |
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