# Kernel of a differential equation

I'm reading the paper entitled 'Existence and properties of travelling waves for the Gross-Pitaevskii equation' by Fabrice Bethuel, Philippe Gravejat and Jean-Claude Saut. At a certain point the paper says:

The Fourier transform of the kernel $$K$$ associated to $$\eta '' + (c^2-2)\eta + 3\eta ^2 = 0$$ is $$\hat{K}(\xi)=\frac{1}{2-c^2+\xi^2}$$ I know what the Fourier transform is, but I don't know exctly what does it mean by kernel associated to $$\eta '' + (c^2-2)\eta + 3\eta ^2 = 0$$. Could anyone help me with this concept?