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On the Cauchy Problem for the Sawada-Kotera Equation: Soliton resolution conjecture, Painlevé transcendents and asymptotic stability
We derive long-time asymptotics in different space-time regions for the Sawada-Kotera (SK) equation with admissible data involving continuous spectrum and finite discrete spectrum. Our result proves the soliton resolution conjecture, yields the asymptotics governed by the F-XVIII Painlevé transcende
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