Geodesic
Elliptic breather for nonlinear Shr\"odinger equation
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 22, Tome 398 (2012), pp. 209-222

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Two-phase elliptic solution of the nonlinear Shrödinger equation is constructed. The conditions on the parameters for the periodic rogue wave solution are given. It is shown that degenerations of this solution lead to Akhmediev breather and to Peregrin soliton. 
@article{ZNSL_2012_398_a10,
     author = {A. O. Smirnov},
     title = {Elliptic breather for nonlinear {Shr\"odinger} equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {209--222},
     publisher = {mathdoc},
     volume = {398},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a10/}
}
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A. O. Smirnov. Elliptic breather for nonlinear Shr\"odinger equation. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 22, Tome 398 (2012), pp. 209-222. http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a10/