Multi-rogue waves solutions to the focusing NLS equation and the KP-I equation

By P. Dubard, V. Matveev. 2011

149 citations recorded by the source corpus.

Abstract. We construct a multi-parametric family of quasi-rational solutions to the focusing NLS equation, presenting a profile of multiple rogue waves. These solutions have also been used by us to construct a large family of smooth, real localized rational solutions of the KP-I equation quite different from the multi-lumps solutions first constructed in Bordag et al. (1977). The physical relevance of both equations is very large. From the point of view of geosciences,the focusing NLS equation is relevant to the description of surface waves in deep water, and the KP-I equation occurs in the description of capillary gravitational waves on a liquid surface, but also when one considers magneto-acoustic waves in plasma (Zhdanov, 1984) etc. In addition, there are plenty of equations of physical importance, having their origin in fiber optics, hydrodynamics, plasma physics and many other areas, which are gauge equivalent to the NLS equation or to the KP-I equation. Therefore our results can be easily extended to a large number of systems of physical interest to be discussed in separate publications.

Subfields: Oceanography, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5a700a9837a5755c63c8db41686daac08e8afb6f

How researchers see this paper

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

In Oceanography

1. Pierre Gaillard
2. Frédéric Dias
3. John M. Dudley
4. Goëry Genty
5. Miro Erkintalo

In Statistical and Nonlinear Physics

1. Pierre Gaillard
2. Abdul-Majid Wazwaz
3. Biao Li
4. Frédéric Dias
5. John M. Dudley
6. Goëry Genty
7. Miro Erkintalo
8. Awatif A. Hendi

Citations in the corpus

• Novel high‐order breathers and rogue waves in the Boussinesq equation via determinants (2019, background): “For larger M in (15), the higher-order solution u describing superposition of M individual first-order solution u defined in (19) can be generated, which are order M breather, order M soliton, or a mixture of an order M1 (M1 < M) breather and an order (M − M1) soliton.”
• Families of quasi-rational solutions of the NLS equation and multi-rogue waves (2011, methodology): “Surprisingly, we recover after reductions exactly the same analytical expression of the solutions given in [6, 8].”
• 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”