Resonance interaction of vector breathers and exotic dynamics in the coupled Hirota equation
This work presents a systematic theoretical investigation of vector breathers and their nonlinear interactions in the coupled Hirota equation. This model describes the simultaneous propagation of ultrashort optical pulses in optical fibers and contains a key parameter that characterizes the strength of higher-order linear and nonlinear effects, such as third-order dispersion and self-steepening. For the model, we focus on the focusing-focusing case. On a nonzero plane-wave background, we derive explicit expressions for multi-breather solutions of the coupled Hirota equation by the dressing method. For the single-breather solution, by choosing special constant vectors, the vector breathers can be classified into three fundamental types: Type I, Type II, and Type III. We then analyze their characteristic parameters, including spatial localization and group velocity, as well as important special cases such as the Kuznetsov-Ma breathers, Peregrine soliton, and Akhmediev type breathers etc. Through the above analysis, we find that the higher-order effect parameter only modifies the propagation velocity and oscillation period of the breathers, while the resonance conditions remain satisfied: when the wave numbers and frequencies match, inelastic resonant interactions can occur between Type I and Type II breathers, manifesting either as a fusion process (I + II \rightarrow II) or the reverse decay process (III \rightarrow I + II). Furthermore, we present the explicit expression for the two breather solutions of the equation and analyze its rich interaction scenarios, including two breather resonances and elastic collisions, and we point out that the special case of resonance corresponds to the limiting case of merging eigenvalues. Finally, we carry out numerical simulations to verify the accuracy of the obtained solutions.