Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrodinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn. Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine's breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.
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Loughborough Univ Technol, Dept Math Sci, Loughborough LE11 3TU, Leics, EnglandLoughborough Univ Technol, Dept Math Sci, Loughborough LE11 3TU, Leics, England
El, G. A.
Khamis, E. G.
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Univ Sao Paulo, Inst Fis, BR-05508090 Sao Paulo, Brazil
Natl Inst Space Res INPE, Ctr Weather Forecasting & Climate Studies CPTEC, Sao Paulo, BrazilLoughborough Univ Technol, Dept Math Sci, Loughborough LE11 3TU, Leics, England
Khamis, E. G.
Tovbis, A.
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Univ Cent Florida, Dept Math, Orlando, FL 32816 USALoughborough Univ Technol, Dept Math Sci, Loughborough LE11 3TU, Leics, England
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Inner Mongolia Normal Univ, Coll Math Sci, Hohhot 010022, Peoples R China
Ctr Appl Math Sci, Hohhot 010022, Inner Mongolia, Peoples R ChinaInner Mongolia Normal Univ, Coll Math Sci, Hohhot 010022, Peoples R China
Shi, Wei
Zhaqilao
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Inner Mongolia Normal Univ, Coll Math Sci, Hohhot 010022, Peoples R China
Ctr Appl Math Sci, Hohhot 010022, Inner Mongolia, Peoples R ChinaInner Mongolia Normal Univ, Coll Math Sci, Hohhot 010022, Peoples R China