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Lax Pair for the Kirchhoff-Pohozaev equation
We prove that the Kirchhoff-Pohozaev equation on any compact connected Riemannian manifold without boundary admits a Lax pair $(L,B)$, where $L$ is a self-adjoint finite-rank perturbation of the Laplace-Beltrami operator and $B$ is a skew-adjoint operator of finite rank, both depending analytically
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