Wronskian Representation of Solutions of NLS Equation, and Seventh Order Rogue Wave

Pierre Gaillard^{*}

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References

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[7] N. Akhmediev, A. Ankiewicz and J. M. Soto-Crespo, “Rogue Waves and Rational Solutions of Nonlinear Schrodinger Equation,” Physical Review E, Vol. 80, 2009, Article ID: 026601.

[8] D. J. Kedziora, A. Ankiewicz and N. Akhmediev, “Circular Rogue Wave Clusters,” Physical Review E, Vol. 84, 2011, Article ID: 056611.

[9] P. Dubard, P. Gaillard, C. Klein and V. B. Matveev, “On Multi-Rogue Waves Solutions of the NLS Equation and Position Solutions of the KdV Equation,” European Physical Journal, Vol. 185, No. 1, 2010, pp. 247-258.
doi:10.1140/epjst/e2010-01252-9

[10] P. Gaillard, “Families of Quasi-Rational Solutions of the NLS Equation and Multi-Rogue Waves,” Journal of Physics A: Mathematical and Theoretical, Vol. 44, No. 43, 2011, pp. 1-15. doi:10.1088/1751-8113/44/43/435204

[11] A. Ankiewicz, N. Akhmediev and P. A. Clarkson, “Rogue Waves, Rational Solutions, the Patterns of Their Zeros and Integral Relations,” Journal of Physics A: Mathematical and Theoretical, Vol. 43, 2010, pp. 1-9

[12] B. Guo, L. Ling and Q. P. Liu, “Nonlinear Schrodinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions,” Physical Review E, Vol. 85, No. 2, 2012, Article ID: 026607.
doi:10.1103/PhysRevE.85.026607

[13] Y. Ohta and J. Yang, “General High-Order Rogue Waves and Their Dynamics in the Nonlinear Schrodinger Equation,” Proceedings of the Royal Society A, Vol. 468, No. 2142, 2012, pp. 1716-1740. doi:10.1098/rspa.2011.0640

[14] P. Gaillard, “Wronskian Representation of Solutions of the NLS Equation and Higher Peregrine Breathers,” Journal of Mathematical Sciences: Advances and Applications, Vol. 13, No. 2, 2012, pp. 71-153.