Critical density of a soliton gas
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solitondensityassociatedboundby-productcriticaldensederivation
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We quantify the notion of a dense soliton gas by establishing an upper bound for the integrated density of states of the quantum-mechanical Schr\"odinger operator associated with the KdV soliton gas dynamics. As a by-product of our derivation we find the speed of sound in the soliton gas with Gaussian spectral distribution function.
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