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General Higher-order Breathers and Rogue Waves in the Two-component Long-wave--short-wave Resonance-interaction Model by Rao, Jiguang; Malomed, Boris A.; Mihalache, Dumitru; He, Jingsong is a scholarly article available to read on EtoBox.

What is General Higher-order Breathers and Rogue Waves in the Two-component Long-wave--short-wave Resonance-interaction Model about?

General higher-order breather and rogue wave (RW) solutions to the two-component long wave--short wave resonance interaction (2-LSRI) model are derived via the bilinear Kadomtsev-Petviashvili hierarchy reduction method and are given in terms of determinants. Under particular parametric conditions, the breather solutions can reduce to homoclinic orbits, or a mixture of breathers and homoclinic orbits. There are three families of RW solutions, which correspond to a simple root, two simple roots, and a double root of an algebraic equation related to the dimension reduction procedure. The first family of RW solutions consists of $\frac{N(N+1)}{2}$ bounded fundamental RWs, the second family is composed of $\frac{N_1(N_1+1)}{2}$ bounded fundamental RWs coexisting with another $\frac{N_2(N_2+1)}{2}$ fundamental RWs of different bounded state ($N,N_1,N_2$ being positive integers), while the third one have ${[\widehat{N}_1^2+\widehat{N}_2^2-\widehat{N}_1(\widehat{N}_2-1)]}$ fundamental bounded RWs ($\widehat{N}_1,\widehat{N}_2$ being non-negative integers). The second family can be regarded as the superpositions of the first family, while the third family can be the degenerate case of the f

Author

Rao, Jiguang; Malomed, Boris A.; Mihalache, Dumitru; He, Jingsong

Published

2022

Language

EN