50 citations · 147 across the 17 of their papers we have counts for
18 papers
On Matrix Valued Schrödinger Operators on the Discrete Real Line: Resolvent Boundary Values, Limiting Absorption Principle, Hölder Regularity and Dispersive Estimates
Ballesteros Miguel, Franco Córdova Gerardo, Gil Jonathan +1
This work establishes new results on spectral theory and time evolution for matrix-valued discrete Schrödinger operators on the space of square-summable matrix sequences. The matri…
Non-flat conformal blow-up profiles for the 1D critical nonlinear Schrödinger equation
Yvan Martel, Ivan Naumkin
For the critical one-dimensional nonlinear Schrödinger equation, we construct blow-up solutions that concentrate a soliton at the origin at the conformal blow-up rate, with a non-f…
Levinson theorem for discrete Schrödinger operators on the line with matrix potentials having a first moment
Miguel Ballesteros, Gerardo Franco Córdova, Ivan Naumkin +1
This paper proves new results on spectral and scattering theory for matrix-valued Schrödinger operators on the discrete line with non-compactly supported perturbations whose first…
The Matrix Nonlinear Schrödinger Equation with a Potential
Ivan Naumkin, Ricardo Weder
This paper is devoted to the study of the large-time asymptotics of the small solutions to the matrix nonlinear Schrödinger equation with a potential on the half-line and with gene…
Asymptotic behavior for a dissipative nonlinear Schrödinger equation
Thierry Cazenave, Zheng Han, Ivan Naumkin
We consider the Schrödinger equation with nonlinear dissipation \begin{equation*} i \partial _t u +Δu=λ|u|^αu \end{equation*} in , , where $λ\in {\mathbb C}…
Sign-changing solutions of the nonlinear heat equation with persistent singularities
Thierry Cazenave, Flávio Dickstein, Ivan Naumkin +1
We study the existence of sign-changing solutions to the nonlinear heat equation on , , with , where…
Local smooth solutions of the nonlinear Klein-gordon equation
Thierry Cazenave, Ivan Naumkin
Given any and , we prove the local existence of arbitrarily smooth solutions of the nonlinear Klein-Gordon equation $\partial_{ tt } u - Δu + μ_1 u =…
estimates for matrix Schrödinger equations
Ivan Naumkin, Ricardo Weder
This paper is devoted to the study of dispersive estimates for matrix Schrödinger equations on the half-line with general boundary condition, and on the line. We prove $L^{p}-L^{p^…
On travelling waves of the non linear Schrödinger equation escaping a potential well
Ivan Naumkin, Pierre Raphäel
In this paper we consider the NLS equation with focusing nonlinearities in the presence of a potential. We investigate the compact soliton motions that correspond to a free soliton…
Estimates in the modulation spaces for the Dirac equation with potential
Keiichi Kato, Ivan Naumkin
In the present paper we obtain estimates in the modulation spaces for the solutions to the Dirac equation with quadratic and sub-quadratic potentials. We derive a representation fo…
Perturbations of self-similar solutions
Thierry Cazenave, Flávio Dickstein, Ivan Naumkin +1
We consider the nonlinear heat equation with , either on , , or on a bounded domain with Dirichlet boundary conditions. We prove th…
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…
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…
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 on , where and . We prove that in the range , for every , there…
Modified scattering for the critical nonlinear Schrödinger equation
Thierry Cazenave, Ivan Naumkin
We consider the nonlinear Schrödinger equation in all dimensions , where and . We construct a class of i…
Local existence, global existence, and scattering for the nonlinear Schrödinger equation
Thierry Cazenave, Ivan Naumkin
In this paper, we construct for every and a space of initial values for which there exists a local solution of the nonlinear Schrödinger equation \begin{eq…
Time delay for the Dirac equation
Ivan Naumkin, Ricardo Weder
We consider time delay for the Dirac equation. A new method to calculate the asymptotics of the expectation values of the operator $\int\limits_{0} ^{\infty}e^{iH_{0}t}ζ\left( \fra…
High-energy and smoothness asymptotic expansion of the scattering amplitude for the Dirac equation and applications
Ivan Naumkin, Ricardo Weder
We obtain an explicit formula for the diagonal singularities of the scattering amplitude for the Dirac equation with short-range electromagnetic potentials. Using this expansion we…