On the Cauchy Problem for the Sawada-Kotera Equation: Soliton resolution conjecture, Painlevé transcendents and asymptotic stability

Zheng-Kang Huang, Shou-Fu Tian

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.…