4 citations · 10 across the 6 of their papers we have counts for
6 papers · 1 filter
Inverse scattering transform for the Kundu-Eckhaus Equation with nonzero boundary condition
Ning Guo, Jian Xu
In this paper, we consider the initial value problem for both of the defocusing and focusing Kundu-Eckhaus (KE) equation with non-zero boundary conditions (NZBCs) at infinity by in…
Long-time asyptotics behavior for the integrable modified Camassa-Holm equation with cubic nonlinearity
Jian Xu, Engui Fan
In this paper, we investigate the long-time asymptotic behavior of the solution to the initial value problem for the modified Camassa-Holm (mCH) equation with cubic nonlinearity. T…
Long-time asymptotics for the Nonlocal mKdV equation
Fengjing He, Engui Fan, Jian Xu
In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation (nonlocal mKdV) \[q_t(x,t)+q_{xxx}(x,t)-6q(x,t)q(-x,-t)q_…
Long-time asymptotics for the short pulse equation
Jian Xu
In this paper, we analyze the long-time behavior of the solution of the initial value problem (IVP) for the short pulse (SP) equation. As the SP equation is a complete integrable s…
The unified method for the three-wave equation on the half-line
Jian Xu, Engui Fan
We present a Riemann-Hilbert problem formalism for the initial-boundary value problem for the three-wave equation: \[p_{ij,t}-\frac{b_i-b_j}{a_i-a_j}p_{ij,x}+\sum_k(\frac{b_k-b_j}{…
The Fokas method to the Sasa-Satsuma equation on the half-line
Jian Xu, Engui Fan
We present a Riemann-Hilbert problem formalism for the initial-boundary value problem for the Sasa-Satsuma(SS) equation: $iq_T+\frac{1}{2}q_{XX}+|q|^2q+i\eps (q_{XXX}+6|q|^2q_X+3q(…