3 papers
math.AP2026
On the Cauchy problem for the Tzitzéica equation: Soliton resolution conjecture and asymptotic analysis
Shou-Fu Tian, Jia-Fu Tong
We study the Cauchy problem for the Tzitzéica equation, which is an important integrable model arising in affine differential geometry and characterizing proper affine spheres. Rec…
math.AP2025
On soliton resolution to Cauchy problem of the spin-1 Gross-Pitaevskii equation
Shou-Fu Tian, Jia-Fu Tong
We investigate the Cauchy problem for the spin-1 Gross-Pitaevskii(GP) equation, which is a model instrumental in characterizing the soliton dynamics within spinor Bose-Einstein con…
math.AP2025
On Cauchy problem to the modified Camassa-Holm equation: Painlevé asymptotics
Jia-Fu Tong, Shou-Fu Tian
We investigate the Painlevé asymptotics for the Cauchy problem of the modified Camassa-Holm (mCH) equation with decaying initial data \begin{align*}\nonumber &m_t+\left((u^2-u_x^2)…