We consider a system of first order coupled mode equations in \({\mathbb {R}}^d\) describing the envelopes of wavepackets in nonlinear periodic media. Under the assumptions of a spectral gap and a generic assumption on the dispersion relation at the spectral edge, we prove the bifurcation of standing gap solitons of the coupled mode equations from the zero solution. The proof is based on a Lyapunov–Schmidt decomposition in Fourier variables and a nested Banach fixed point argument. The reduced bifurcation equation is a perturbed stationary nonlinear Schrödinger equation. The existence of solitary waves follows in a symmetric subspace thanks to a spectral stability result. A numerical example of gap solitons in \({\mathbb {R}}^2\) is provided.

我们考虑\（{\ mathbb {R}} ^ d \）中的一阶耦合模式方程系统，该系统描述了非线性周期介质中波包的包络。在光谱间隙的假设和在光谱边缘的色散关系的一般假设下，我们从零解证明了耦合模式方程的站立间隙孤子的分歧。该证明基于傅立叶变量的Lyapunov–Schmidt分解和嵌套的Banach不动点参数。简化的分叉方程是扰动的非线性薛定ding方程。由于频谱稳定的结果，孤立波的存在遵循对称子空间。提供了\（{\ mathbb {R}} ^ 2 \）中的间隙孤子的数值示例。