Nonlinear steady-state waves are obtained by the amplitude-based Homotopy Analysis Method (AHAM) when resonances among surface gravity waves are considered in water of finite depth. AHAM, newly proposed in this paper within the context of Homotopy Analysis Method (HAM) and well validated in various ways, is able to deal with nonlinear wave interactions. In waves with small propagation angles, it is confirmed that more components share the wave energy if the wave field has a greater steepness. However, in waves with larger propagation angles, it is newly found that wave energy may also concentrate in some specific components. In such wave fields, off-resonance detuning is also considered. Bifurcation and symmetrical properties are discovered in some wave fields. Our results may provide a deeper understanding on nonlinear wave interactions at resonance in water of finite depth.

当在有限深度的水中考虑表面重力波之间的共振时，通过基于振幅的同伦分析方法（AHAM）获得非线性稳态波。本文在同伦分析方法（HAM）的背景下新提出的AHAM能够以非线性方式处理非线性波相互作用。在传播角小的波中，如果波场具有更大的陡度，则可以确认更多的分量共享波能。然而，在具有较大传播角的波中，新发现波能也可能集中在某些特定分量上。在这种波场中，还考虑了失谐失谐。在某些波场中发现了分叉和对称性质。