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Nonlinear Schrödinger equation: Generalized Darboux transformation and rogue wave solutions
Physical Review E · 2012 · Vol. 85(2) · pp. 026607–026607
Boling Guo✉(Institute of Applied Physics and Computational Mathematics)Liming Ling(Institute of Applied Physics and Computational Mathematics)Q.P. Liu(China University of Mining and Technology)
Abstract
In this paper, we construct a generalized Darboux transformation for the nonlinear Schrödinger equation. The associated N-fold Darboux transformation is given in terms of both a summation formula and determinants. As applications, we obtain compact representations for the Nth-order rogue wave solutions of the focusing nonlinear Schrödinger equation and Hirota equation. In particular, the dynamics of the general third-order rogue wave is discussed and shown to exhibit interesting structures.
Nonlinear Waves and SolitonsNonlinear Photonic SystemsFractional Differential Equations SolutionsRogue waveTransformation (genetics)Nonlinear systemNonlinear Schrödinger equationMathematicsMathematical physicsSchrödinger equationDarboux integralOrder (exchange)Lax pair
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957
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References
Rogue waves and rational solutions of the Hirota equation
Physical Review E · 2010 · 507 citations
Rogue waves and rational solutions of the nonlinear Schrödinger equation
Physical Review E · 2009 · 1,003 citations
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