Vector rogue waves on a double-plane wave background

Abstract

We study rogue wave excitation dynamics on a double-plane wave background through deriving rogue wave solution on the background. The results indicate that rogue wave still can be excited successfully from resonant perturbations with the two plane wave backgrounds. The obtained vector rogue wave can be decomposed to two rogue waves located on the two backgrounds separately. This enables us to investigate the superpositions of two of the three well-known fundamental rogue wave patterns, mainly including eye-shaped, anti-eye-shaped, and four-petaled one. The explicit conditions for different possible superpositions are clarified by a phase diagram for rogue wave pattern on each plane wave background. The detail analysis indicate that the rogue wave admits many different profiles, in contrast to the ones reported before. The studies can be extended directly to investigate other localized waves on double-plane wave background and even more plane waves involved cases. PACS numbers: 05.45.Yv, 02.30.Ik, 42.65.TgIntroduction-Rogue wave (RW) depicts a unique event that seems to appear from nowhere and disappear without a trace, and can appear in a variety of different contexts [1][2][3][4][5][6][7]. The rational solutions on one plane wave background of related dynamics equations have been used to describe RW phenomena widely, which is supported by many experiments [8][9][10][11]. According to the component number, RW can be classified to scalar RW [12][13][14][15][16][17][18], and vector RW [19][20][21][22][23][24]. Most of previous RWs are excited on one plane wave background. But there are usually more than one plane wave backgrounds in complex systems. Then, if the background field contain more plane waves, can the RWs still exist or would the RW evolution characters be kept? We would like to study on this question through revisiting on the vector RWs, since the scalar RW system usually do not admit plane wave superposition background, and vector system could admit plane wave superposition form.Vector RW has been studied widely on a plane wave background [20][21][22][23][24][25]. It has been shown that vector RWs admit more complex and abundant excitation patterns than the scalar ones. Anti-eye-shaped RW and four-petaled RW were reported in vector systems. We still choose a standard two-component coupled nonlinear Schrödinger equations (NLSE) to discuss the vector RW dynamics, because of its wide applications in physical systems [26,27]. It is noted that the coupled NLSE can admit cosine or sine type seed solution, which can be decomposed to a double-plane wave background (DPWB). This provides possibilities to investigate RWs on a DPWB in detail.In this paper, we obtain the vector RW excitations on a DPWB with the aid of Darboux transformation. The results indicate that RW still can be excited successfully from resonant perturbations with the two plane

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