New type of rogue waves

Ustinov N.V.

Joint Institute for Nuclear Research, Laboratory of Radiation Biology, Joliot-Curie St. 6, Dubna, 141980, Russia, E-mail:

The investigation of rogue waves in various fields of physics has been of the great interest to the researchers for many years (see review [1] and the literature therein). Various mechanisms were proposed to explain an appearance of these waves. The occurrence of rogue waves is most often considered on the basis of mechanisms of the modulation instability and the superposition of waves. In both cases, the formation of rogue waves occurs against the background of a wave field, which is reflected in the definitions of these waves [1].

In this report, a new type of rogue waves is presented for the case of the two-dimensional multicomponent generalization of the Yajima–Oikawa system [2, 3]. A distinctive feature of the waves of this type is that their formation occurs in the absence of the background waves. In addition, the evolution of the waves considered has a two-dimensional character. The generating mechanism of rogue waves of this type is nonlinear focusing. A method for obtaining the solutions of the two-dimensional multicomponent generalization of the Yajima–Oikawa system in the form of rogue waves of the new type and their properties are presented in [4].

The results obtained may stimulate the further studies of rogue waves. It seems important to extend the approach leading to this type of rogue waves to other models of different physical contexts describing the wave interactions.


1. Slunyaev A.V., Pelinovsky D.E., Pelinovsky E.N. Rogue waves in the sea: observations, physics, and mathematics // Phys. Usp. Vol 66, No. 2, 2023. Pp. 148-172.

2. Kanna T., Vijayajayanthi M., Lakshmanan M. Mixed solitons in (2+1) dimensional multicomponent long-wave‒short-wave system // Phys. Rev. E, Vol. 90, No. 4, 2014. Art. no. 042901 (15 pages).

3. Sazonov S.V., Ustinov N.V. Two-dimensional dynamics of solitons under the conditions of Zakharov‒Benney resonance // Bulletin of RAS: Phys. Vol. 82, No. 11, 2018. Pp. 1359-1362.

4. Ustinov N.V. New type of rogue waves //


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