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?

Thanks you in advance.


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