5 papers · 1 filter
On dispersive decay for the generalized Korteweg--de Vries equation
Matthew Kowalski, Minjie Shan
We prove pointwise-in-time dispersive estimates for solutions to the generalized Korteweg--de Vries (gKdV) equation. In particular, for solutions to the mass-critical model, we ass…
Global asymptotic behavior of solutions to the generalized derivative nonlinear Schrödinger equation
Minjie Shan
This article is concerned with the global asymptotic behavior for the generalized derivative nonlinear Schrödinger (gDNLS) equation. When the nonlinear effect is not strong, we sh…
Dispersive decay for the mass-critical generalized Korteweg-de Vries equation and generalized Zakharov-Kuznetsov equations
Minjie Shan
In this paper, we discuss pointwise decay estimate for the solution to the mass-critical generalized Korteweg-de Vries (gKdV) equation with initial data $u_0\in H^{1/2}(\mathbb{R})…
The propagation of regularity and dispersive blow-up phenomenon to higher-order generalized KdV equations
Minjie Shan
Some special properties of smoothness and singularity concerning to the initial value problem associated with higher-order generalized KdV equations are investigated. On one hand,…
Dispersive blow-up for solutions to three dimensional generalized Zakharov-Kuznetsov equations
Yingzhe Ban, Minjie Shan
We illustrate the dispersive blow up phenomena of the solutions of three dimensional generalized Zakharov-Kuznetsov equations. In particular, we construct smooth initial data such…