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Singularity Structure Analysis of the Vector Nonlinear Schrodinger System: Miscellaneous Excitations and their Interactions (pp.181-220) $100.00
Authors:  (Victor Kuetche Kamgangr, Thomas Boueton Bouetou, Crepin Kofane Timoleon, Ecole Nationale Superieure Polytechnique, University of Yaounde I, Cameroon, and others)
Abstract:
Throughout this chapter, we investigate the singularity structure analysis of the
(2+1)-dimensional coupled nonlinear Schr¨odinger (CNLS) equations, and we show
that these equations are Painlev´e (P)-integrable. Bymeans of theWeiss et al.’smethodology,
we show the arbitrariness of the expansion coefficients and the consistency of
the truncation corresponding to a special B¨acklund transformation (BT) of these CNLS
equations. In the wake of such transformation, following the Hirota’s formalism, we
derive a one-soliton solution. Besides, by using the Zakharov-Shabat (ZS) scheme
which provides a general Lax-representation of an evolution system, we show that the
(2+1)-dimensional CNLS system under interests is completely integrable. Furthermore,
using the arbitrariness of the above coefficients, we unearth and investigate a
typical spectrum of localized and periodic coherent structures. As a result, we depict
the elastic and nonelastic interactions amongst such structures and also a splitting
phenomenon occurring during their motion. 


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Singularity Structure Analysis of the Vector Nonlinear Schrodinger System: Miscellaneous Excitations and their Interactions (pp.181-220)