Taiyang Xu

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20242026

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math.AP2026

On the large-time asymptotics of the defocusing mKdV equation with step-like initial data

Taiyang Xu, Yidan Zhang

We study the Cauchy problem for the defocusing modified Korteweg-de Vries (mKdV) equation with step-like initial data approaching nonzero constants $c_{l}$ and $c_{r}$ as $x \to -\inft…

math.AP2025

Soliton resolution and asymptotic stability of $N$ -soliton solutions for the defocusing mKdV equation with a non-vanishing background

Zechuan Zhang, Taiyang Xu, Engui Fan

We analytically study the large-time asymptotics of the solution of the defocusing modified Korteweg-de Vries (mKdV) equation under a symmetric non-vanishing background, which supp…

math.AP2024

Transient asymptotics of the modified Camassa-Holm equation

Taiyang Xu, Yiling Yang, Lun Zhang

We investigate long time asymptotics of the modified Camassa-Holm equation in three transition zones under a nonzero background. The first transition zone lies between the soliton…

On the large-time asymptotics of the defocusing mKdV equation with step-like initial data

Soliton resolution and asymptotic stability of N-soliton solutions for the defocusing mKdV equation with a non-vanishing background

Transient asymptotics of the modified Camassa-Holm equation

Soliton resolution and asymptotic stability of $N$ -soliton solutions for the defocusing mKdV equation with a non-vanishing background