S. Roudenko

activity

20062026

most citedA sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation

307 citations · 580 across the 47 of their papers we have counts for

collaborators

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44 papers · 1 filter

math.AP2026

Local well-posedness for the biharmonic nonlinear Schrödinger equation in low dimensions

Iryna Petrenko, Oscar Riaño, Svetlana Roudenko

In this paper we consider the 4th order (or biharmonic) nonlinear Schrödinger (NLS) equation in dimensions 1, 2, and 3, where the potential term is expressed as a power non-lineari…

math.AP2026

Review of well-posedness methods for the 1D nonlinear Schrödinger equation with an application to combined nonlinearities

Alex D. Rodriguez, Gia Azcoitia, Hannah Wubben +1

We consider the nonlinear Schrödinger equation in one dimension with nonlinearities of type $∣ u ∣^{α} u$ for any power $α > 0$ and review two different methods for obtaining solutions, n…

math.AP2026

The nonlinear Schrödinger equation with combined nonlinearities in 1D

Oscar Riaño, Alex D Rodriguez, Svetlana Roudenko

We consider the one-dimensional nonlinear Schrödinger equation $i u_{t} + u_{xx} + N (u) u = 0, x, t \in R,$ with the nonlinearity term that is expressed as a s…

math.AP2025

Well-posedness of the focusing stochastic nonlinear Schrödinger equation: $L^{2}$ -critical and supercritical cases

Annie Millet, Svetlana Roudenko

We study the focusing $L^{2}$ -critical and supercritical stochastic nonlinear Schrödinger equation subject to additive or multiplicative noise. We investigate global or long time beh…

math.AP2025

Nonlinear Schrödinger equation on a unit ball in one and two dimensions

Christian Klein, Svetlana Roudenko, Nikola Stoilov

We investigate the nonlinear Schrödinger equation on a unit ball in one and two dimensions with Dirichlet boundary condition, focusing on ground states, their limiting behavior, st…

math.AP2024

Dichotomy Results for the Electromagnetic Schrödinger Equation

Magdalena Czubak, Ian Miller, Svetlana Roudenko

The electromagnetic nonlinear Schrödinger (emNLS) equation is a variant of the well-studied nonlinear Schrödinger equation. In this article, we consider questions of global existen…

math.AP2024

On the well-posedness of the periodic fractional Schrödinger equation

Beckett Sanchez, Oscar Riaño, Svetlana Roudenko

We consider the periodic fractional nonlinear Schrödinger equation $i u_{t} - (- Δ)^{\frac{s}{2}} u + N (∣ u ∣) u = 0, x \in T^{N}, t \in R, s > 0,$ …

math.AP2022

Threshold solutions for the Hartree equation

Anudeep K. Arora, Svetlana Roudenko

We consider the focusing $5$ d Hartree equation, which is $L^{2}$ -supercritical, with finite energy initial data, and investigate the solutions at the mass-energy threshold. We establ…

math.AP2022★ 3 cited

Stability and instability of solitary waves in fractional generalized KdV equation in all dimensions

Oscar Riaño, Svetlana Roudenko

We study stability of solitary wave solutions for the fractional generalized Korteweg-de Vries equation $$ \partial_t u- \partial_{x_1} D^αu+ \tfrac{1}{m}\partial_{x_1}(u^m)=0, ~ (…

math.AP2022★ 8 cited

Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity

Isaac Friedman, Oscar Riaño, Svetlana Roudenko +2

We consider two types of the generalized Korteweg - de Vries equation, where the nonlinearity is given with or without absolute values, and, in particular, including the low powers…

math.AP2021

Higher dimensional generalization of the Benjamin-Ono equation: 2D case

Oscar Riaño, Svetlana Roudenko, Kai Yang

We consider a higher-dimensional version of the Benjamin-Ono (HBO) equation in the 2D setting: $u_{t} - R_{1} Δ u + \frac{1}{2} (u^{2})_{x} = 0, (x, y) \in R^{2}$ , which is $L^2…

math.AP2021

Interaction with an obstacle in the 2d focusing nonlinear Schrödinger equation

Oussama Landoulsi, Svetlana Roudenko, Kai Yang

We present a numerical study of solutions to the $2 d$ cubic and quintic focusing nonlinear Schrödinger equation in the exterior of a smooth, compact and strictly convex obstacle (a…

math.AP2020★ 9 cited

Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation

C. Klein, S. Roudenko, N. Stoilov

We present a detailed numerical study of solutions to the Zakharov-Kuznetsov equation in three spatial dimensions. The equation is a three-dimensional generalization of the Kortewe…

math.AP2020★ 14 cited

Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study

Svetlana Roudenko, Zhongming Wang, Kai Yang

We consider the generalized Benjamin-Ono (gBO) equation on the real line, $u_{t} + \partial_{x} (- H u_{x} + \frac{1}{m} u^{m}) = 0, x \in R, m = 2, 3, 4, 5$ , and perform nu…

math.AP2020

Well-posedness in weighted spaces for the generalized Hartree equation with $p < 2$

Anudeep K. Arora, Oscar Riaño, Svetlana Roudenko

We investigate the well-posedness in the generalized Hartree equation $i u_{t} + Δ u + (∣ x ∣^{- (N - γ)} * ∣ u ∣^{p}) ∣ u ∣^{p - 2} u = 0$ , $x \in R^{N}$ , $0 < γ < N$ , for low powers of nonlinea…

math.AP2020

Threshold solutions for the nonlinear Schrödinger equation

Luccas Campos, Luiz Gustavo Farah, Svetlana Roudenko

We study the focusing NLS equation in $R^{N}$ in the mass-supercritical and energy-subcritical (or intercritical) regime, with $H^{1}$ data at the mass-energy threshold $ \mat…

math.AP2020★ 10 cited

Threshold solutions in the focusing 3D cubic NLS equation outside a strictly convex obstacle

Thomas Duyckaerts, Oussama Landoulsi, Svetlana Roudenko

We study the dynamics of the focusing $3 d$ cubic nonlinear Schrödinger equation in the exterior of a strictly convex obstacle at the mass-energy threshold, namely, when $ E_Ω[u_0]…

math.AP2020★ 2 cited

Behavior of solutions to the 1D focusing stochastic nonlinear Schrödinger equation with spatially correlated noise

Annie Millet, Alex D Rodriguez, Svetlana Roudenko +1

We study the focusing stochastic nonlinear Schrödinger equation in one spatial dimension with multiplicative noise, driven by a Wiener process white in time and colored in space, i…

math.AP2020★ 2 cited

Asymptotic stability of solitary waves of the 3D quadratic Zakharov-Kuznetsov equation

Luiz Gustavo Farah, Justin Holmer, Svetlana Roudenko +1

We consider the quadratic Zakharov-Kuznetsov equation $\partial_{t} u + \partial_{x} Δ u + \partial_{x} u^{2} = 0$ on $R^{3}$ . A solitary wave solution is given by $Q (x - t, y, z)$ , w…

math.AP2020★ 11 cited

Behavior of solutions to the 1D focusing stochastic $L^{2}$ -critical and supercritical nonlinear Schrödinger equation with space-time white noise

Annie Millet, Svetlana Roudenko, Kai Yang

We study the focusing stochastic nonlinear Schrödinger equation in 1D in the $L^{2}$ -critical and supercritical cases with an additive or multiplicative perturbation driven by space-…

math.AP2020★ 21 cited

Numerical study of Zakharov-Kuznetsov equations in two dimensions

C. Klein, S. Roudenko, N. Stoilov

We present a detailed numerical study of solutions to the (generalized) Zakharov-Kuznetsov equation in two spatial dimensions with various power nonlinearities. In the $L^{2}$ -subc…

math.AP2020★ 2 cited

Stable blow-up dynamics in the $L^{2}$ -critical and $L^{2}$ -supercritical generalized Hartree equation

Kai Yang, Svetlana Roudenko, Yanxiang Zhao

We study stable blow-up dynamics in the generalized Hartree equation with radial symmetry, a Schrödinger-type equation with a nonlocal, convolution-type nonlinearity: $iu_t+Δu +\le…

math.AP2019★ 2 cited

On well-posedness and blow-up in the generalized Hartree equation

Anudeep K. Arora, Svetlana Roudenko

We study the generalized Hartree equation, which is a nonlinear Schrödinger-type equation with a nonlocal potential $iu_t + Δu + (|x|^{-b} \ast |u|^p)|u|^{p-2}u=0, x \in \mathbb{R}…

math.AP2019★ 18 cited

Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation

Debdeep Bhattacharya, Luiz Gustavo Farah, Svetlana Roudenko

We consider the modified Zakharov-Kuznetsov (mZK) equation in two space dimensions in both focusing and defocusing cases. Using the $I$ -method, we prove the global well-posedness o…

Local well-posedness for the biharmonic nonlinear Schrödinger equation in low dimensions

Review of well-posedness methods for the 1D nonlinear Schrödinger equation with an application to combined nonlinearities

The nonlinear Schrödinger equation with combined nonlinearities in 1D

Well-posedness of the focusing stochastic nonlinear Schrödinger equation: L2-critical and supercritical cases

Nonlinear Schrödinger equation on a unit ball in one and two dimensions

Dichotomy Results for the Electromagnetic Schrödinger Equation

On the well-posedness of the periodic fractional Schrödinger equation

Threshold solutions for the Hartree equation

Stability and instability of solitary waves in fractional generalized KdV equation in all dimensions

Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity

Higher dimensional generalization of the Benjamin-Ono equation: 2D case

Interaction with an obstacle in the 2d focusing nonlinear Schrödinger equation

Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation

Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study

Well-posedness in weighted spaces for the generalized Hartree equation with p<2

Threshold solutions for the nonlinear Schrödinger equation

Threshold solutions in the focusing 3D cubic NLS equation outside a strictly convex obstacle

Behavior of solutions to the 1D focusing stochastic nonlinear Schrödinger equation with spatially correlated noise

Asymptotic stability of solitary waves of the 3D quadratic Zakharov-Kuznetsov equation

Behavior of solutions to the 1D focusing stochastic L2-critical and supercritical nonlinear Schrödinger equation with space-time white noise

Numerical study of Zakharov-Kuznetsov equations in two dimensions

Stable blow-up dynamics in the L2-critical and L2-supercritical generalized Hartree equation

On well-posedness and blow-up in the generalized Hartree equation

Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation

Well-posedness of the focusing stochastic nonlinear Schrödinger equation: $L^{2}$ -critical and supercritical cases

Well-posedness in weighted spaces for the generalized Hartree equation with $p < 2$

Behavior of solutions to the 1D focusing stochastic $L^{2}$ -critical and supercritical nonlinear Schrödinger equation with space-time white noise

Stable blow-up dynamics in the $L^{2}$ -critical and $L^{2}$ -supercritical generalized Hartree equation