4 papers · 1 filter
On the Cauchy problem for the Tzitzéica equation: Soliton resolution conjecture and asymptotic analysis
Shou-Fu Tian, Jia-Fu Tong
We prove the soliton resolution conjecture for the Tzitzéica equation, which is an important integrable model arising in affine differential geometry and characterizing proper affi…
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…
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)…
The integrable nonlocal nonlinear Schrödinger equation with oscillatory boundary conditions: long-time asymptotics
Yan Rybalko, Dmitry Shepelsky, Shou-Fu Tian
We consider the Cauchy problem for the integrable nonlocal nonlinear Schrödinger equation \[ \I q_{t}(x,t)+q_{xx}(x,t)+2 q^{2}(x,t)\bar{q}(-x,t)=0, \] subject to the step-like init…