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The proof shows response quasi-periodic solutions exist in relation to transport operators, suggesting these results have broad implications in mathematical physics.
We prove the existence of response quasi-periodic solutions for the forced inviscid Burgers-Hilbert equation, close to any fixed, nonzero constant velocity, provided that the forced term is small enough and the frequency belongs to a Borel set with asymptotically full Lebesgue measure. The proof is based on a reduction of transport operators and Nash-Moser iteration.
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Zhou et al. (2025) studied this question.
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