I. Naumkin

activity

20132026

most citedModified scattering for the critical nonlinear Schrödinger equation

50 citations · 147 across the 17 of their papers we have counts for

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Showing 2017 · math.APShow all

4 papers · 2 filters

math.AP2017

On small travelling waves to the mass critical fractional NLS

Ivan Naumkin, Pierre Raphaël

We consider the mass critical fractional (NLS). We show the existence of travelling waves for all mass below the ground state mass, and give a complete description of the associate…

math.AP2017

Nonlinear Schrödinger equations with exceptional potentials

Ivan Naumkin

We consider the cubic nonlinear Schrödinger equation with an exceptional potential. We obtain a sharp time decay for the global in time solution and we get the large time asymptoti…

math.AP2017★ 11 cited

Sign-changing self-similar solutions of the nonlinear heat equation with positive initial value

Thierry Cazenave, Flávio Dickstein, Ivan Naumkin +1

We consider the nonlinear heat equation $u_{t} - Δ u = ∣ u ∣^{α} u$ on $R^{N}$ , where $α > 0$ and $N \geq 1$ . We prove that in the range $0 < α < \frac{4}{N - 2}$ , for every $μ > 0$ , there…

math.AP2017★ 50 cited

Modified scattering for the critical nonlinear Schrödinger equation

Thierry Cazenave, Ivan Naumkin

We consider the nonlinear Schrödinger equation $i u_{t} + Δ u = λ ∣ u ∣^{\frac{2}{N}} u$ in all dimensions $N \geq 1$ , where $λ \in C$ and $ℑ λ \leq 0$ . We construct a class of i…