On multi-rogue wave solutions of the NLS equation and positon solutions of the KdV equation

By P. Dubard, Pierre Gaillard, Christian Klein, V. Matveev. 2010

301 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9fe0e9163750bf9b6a40879d2aa6008ed0f0f978

How researchers see this paper

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

In Mathematical Physics

1. Jianke Yang
2. Deniz Bilman
3. Peter D. Miller
4. Vladimir V. Konotop
5. Dmitry A. Zezyulin
6. Bo Yang

In Statistical and Nonlinear Physics

1. Jianke Yang
2. Dmitry A. Zezyulin
3. Yasuhiro Ohta
4. Deniz Bilman
5. Peter D. Miller
6. Vladimir V. Konotop
7. Frédéric Dias
8. John M. Dudley

Citations in the corpus

• A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation (2017, background): “8 (see [17, 21, 22, 26] for similar plots) suggest the following questions: Can one determine the asymptotic properties of the peaks and zeros of k.”
• Instabilities, breathers and rogue waves in optics (2014, methodology): “iterion for rogue waves in an MI field seeded by noise is generally only satisfied by particular higher-order SFB solutions (sometimes referred to as “multirogue waves” or “higher-order rogue waves”) [25, 26, 27, 28]. 6 Before discussing noise-seeded MI in detail, we first describe these SFBs and br”
• General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation (2011, background): “If other values of these free parameters are taken, however, these general rogue waves can exhibit other solution dynamics such as arrays of fundamental (Peregrine) rogue waves arising at different times and spatial positions.”
• 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, unknown): “with ζk = −ωkx + 2iωkΩkt + ζ0 k , (17) where Ωk are complex parameters and ωk, ζ0 k are real parameters and the parameters Ωk and ωk satisfy the parametric condition 12Ω(2)k + ω 2 k = 1, (18) for k = 1, 2, .”