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Natural Hazards and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 11, issue 3
Nat. Hazards Earth Syst. Sci., 11, 667–672, 2011
https://doi.org/10.5194/nhess-11-667-2011
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.

Special issue: Extreme and rogue waves

Nat. Hazards Earth Syst. Sci., 11, 667–672, 2011
https://doi.org/10.5194/nhess-11-667-2011
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 03 Mar 2011

Research article | 03 Mar 2011

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

P. Dubard and V. B. Matveev P. Dubard and V. B. Matveev
  • IMB, Université de Bourgogne, 9 av. Alain Savary, Dijon, France

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.

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