307 citations · 1.2k across the 45 of their papers we have counts for
4 papers · 2 filters
Instability of solitons in the 2d cubic Zakharov-Kuznetsov equation
Luiz Gustavo Farah, Justin Holmer, Svetlana Roudenko
We consider the two dimensional generalization of the Korteweg-de Vries equation, the generalized Zakharov-Kuznetsov (ZK) equation, $u_t + \partial_{x_1}(Δu + u^p) = 0, (x_1,x_2) \…
Instability of solitons - revisited, II: the supercritical Zakharov-Kuznetsov equation
Luiz Gustavo Farah, Justin Holmer, Svetlana Roudenko
We revisit the phenomenon of instability of solitons in the two dimensional generalization of the Korteweg-de Vries equation, the generalized Zakharov-Kuznetsov (ZK) equation, $u_t…
Instability of solitons - revisited, I: the critical generalized KdV equation
Luiz Gustavo Farah, Justin Holmer, Svetlana Roudenko
We revisit the phenomenon of instability of solitons in the generalized Korteweg-de Vries equation, . It is known that solitons are unstable for…
Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity II: Supercritical blow-up profiles
Justin Holmer, Chang Liu
We consider the 1D nonlinear Schrödinger equation (NLS) with focusing \emph{point nonlinearity}, where is the delta functio…