The exactly and nearly class-I Bragg resonances of strongly nonlinear waves are studied analytically by the homotopy analysis method. Two types of equilibrium states with time-independent wave spectra and different energy distributions are obtained. Effects of the incident wave height, the seabed height, and the frequency detuning on resonant waves are investigated. Bifurcation points of the equilibrium states are found and tend to greater value of relatively incident wave height for a steeper wave. The wave steepness of the whole wave system grows linearly with the seabed height. Meanwhile, the resonant peak can shift to up or down side when the near resonance is considered. This work provides us a deeper understanding on class-I Bragg resonance and enlightens further studies of higher-order wave-bottom interactions.

中文翻译：

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在完全和几乎I类布拉格共振下具有有限振幅的平衡态

用同伦分析法对强非线性波的精确和接近Ⅰ类布拉格共振进行了研究。得到了两种具有与时间无关的波谱和不同能量分布的平衡态。研究了入射波高度，海床高度和频率失谐对共振波的影响。发现了平衡态的分叉点，并且对于较陡的波，趋向于增加相对入射波高的值。整个波浪系统的波浪陡度随海床高度线性增长。同时，当考虑到近共振时，共振峰可以向上或向下偏移。这项工作使我们对I类布拉格共振有了更深入的了解，并启发了对高阶波底相互作用的进一步研究。