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29 March 2024
 
  » arxiv » nlin/0702010

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Exact solutions to the focusing nonlinear Schrodinger equation
Tuncay Aktosun ; Francesco Demontis ; Cornelis van der Mee ;
Date 7 Feb 2007
Subject Exactly Solvable and Integrable Systems
AbstractA method is presented to construct certain explicit solutions to the focusing cubic nonlinear Schr"odinger equation on the line. Such solutions involve algebraic combinations of polynomials, trigonometric functions, and exponential functions of $x$ and $t.$ In a particular case, the analytic extensions of such solutions to the entire $xt$-plane yield soliton solutions where the number of solitons, the multiplicity of poles, and the norming constants are easily specified. In the general case, such solutions are well behaved in those regions in the $xt$-plane where a key determinant function is nonzero. The compact form of such solutions via matrix exponentials makes their symbolic and numerical evaluations easy.
Source arXiv, nlin/0702010
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