307 citations · 580 across the 47 of their papers we have counts for
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Blow-up dynamics and spectral property in the -critical nonlinear Schrödinger equation in high dimensions
Kai Yang, Svetlana Roudenko, Yanxiang Zhao
We study stable blow-up dynamics in the -critical nonlinear Schrödinger equation in high dimensions. First, we show that in dimensions to generic blow-up behavior…
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) \…
Generalized KdV equation subject to a stochastic perturbation
Annie Millet, Svetlana Roudenko
We prove global well-posedness of the subcritical generalized Korteweg-de Vries equation (the mKdV and the gKdV with quartic power of nonlinearity) subject to an additive random pe…
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…