Rogue waves and rational solutions of the nonlinear Schrödinger equation.

By Nail Akhmediev, Adrian Ankiewicz, José-María Soto-Crespo. Physical review. E, Statistical, nonlinear, and soft matter physics, 2009

937 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/74c7f07d016b5adb8b29f944a9b4bfe13b8ac97e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Jianke Yang
2. Sergei K. Turitsyn
3. Dmitry A. Zezyulin
4. Goëry Genty
5. John M. Dudley
6. Vladimir V. Konotop
7. Yasuhiro Ohta
8. Pierre Gaillard

In Statistical and Nonlinear Physics

1. Jianke Yang
2. Sergei K. Turitsyn
3. John M. Dudley
4. Yasuhiro Ohta
5. Dmitry A. Zezyulin
6. Goëry Genty
7. M. Onorato
8. Frédéric Dias

Citations in the corpus

• Rogue waves and their generating mechanisms in different physical contexts (2013, background): “The NLS solutions associated with such mechanism are known as higher order solutions [65,69–72].”
• Families of quasi-rational solutions of the NLS equation and multi-rogue waves (2011, methodology): “We recover the result of Akhmediev formulated in [1] in the case of the initial condition t = 0.”
• Nonlinear waves in PT -symmetric systems (2016, background): “They 38 can be readily obtained from higher-order rogue waves of the NLS equation through the reduction (109)–(110) (Akhmediev, Ankiewicz, and Soto-Crespo, 2009; Dai and Huang, 2014; Dubard et al., 2010; Guo, Ling, and Liu, 2012; Ohta and Yang, 2012).”
• Novel high‐order breathers and rogue waves in the Boussinesq equation via determinants (2019, neutral): “Fk,k = ⎜⎜⎝ − i ωkek − i ωk i Ωk+Ωk−ωk i Ωk+Ωk+ωk i ωke ζ∗ k + i ωk ⎟⎟⎠ ,Fk,l = ⎜⎜⎜⎝ i (Ωk−Ωl)− ωk+ωl 2 i (Ωk+Ωl )− ωk+ωl 2 i (Ωk+Ωl)+ ωk+ωl 2 i (Ωk−Ω ∗ l )+ ωk+ωl 2 ⎟⎟⎟⎠ , (16)”
• Recent progress in investigating optical rogue waves (2013, background): “When excited from special initial conditions, we can expect excitation of higher-order rogue wave structures [61–63] described by the higher-order rational solutions of the nonlinear Schrödinger equation [64–69] or its extensions such as”
• Higher-order integrable evolution equation and its soliton solutions (2014, neutral): “[16] N.”
• A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation (2017, methodology): “Moreover, the method also makes taking limits [2] or related constructions such as the generalized form of the Darboux transformation [23] unnecessary in generating high-order rogue waves from the background field, and it yields an analytical setting in which the large-N asymptotics ofN th-order rog”