Geodesic
Toward a~classification of quasirational solutions of the~nonlinear
Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 1, pp. 48-58

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Based on a representation in terms of determinants of the order $2N$, we attempt to classify quasirational solutions of the one-dimensional focusing nonlinear Schrödinger equation and also formulate several conjectures about the structure of the solutions. The se solutions can be written as a product of a $t$-dependent exponential times a quotient of two $N(N{+}1)$th degree polynomials in $x$ and $t$ depending on $2N{-}2$ parameters. It is remarkable that if all parameters are equal to zero in this representation, then we recover the $P_N$ breathers.
Keywords: nonlinear Schrödinger equation, determinant, Peregrine breather
Mots-clés : rogue wave. 
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     author = {P. Gaillard},
     title = {Toward a~classification of quasirational solutions of the~nonlinear},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {48--58},
     publisher = {mathdoc},
     volume = {189},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_189_1_a3/}
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P. Gaillard. Toward a~classification of quasirational solutions of the~nonlinear. Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 1, pp. 48-58. http://geodesic.mathdoc.fr/item/TMF_2016_189_1_a3/