Guillaume Rialland

activity

20232026

most citedAsymptotic stability of solitary waves for the 1D near-cubic non-linear Schrödinger equation in the absence of internal modes

2 citations · 3 across the 4 of their papers we have counts for

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math.AP2026

Existence of traveling waves for the two-dimensional Zakharov system

Guillaume Rialland

Via a fixed point argument, we construct solitary waves for the two-dimensional Zakharov system that travel with any small speed $c \in R^{2}$ . Moreover, we investigate thei…

math.AP2025

Non-existence of internal mode for small solitary waves of the 1D Zakharov system

Yvan Martel, Guillaume Rialland

We prove that the linearised operator around any sufficiently small solitary wave of the one-dimensional Zakharov system has no internal mode. This spectral result, along with its…

math.AP2024

Multi-solitary waves for the one-dimensional Zakharov system

Guillaume Rialland

Given different speeds $c_{1}$ , ... , $c_{K}$ , in the present paper we establish the existence of a solution to the Zakharov system in dimension 1 that behaves asymptotically like a $…

math.AP2024★ 1 cited

Asymptotic stability of solitons for near-cubic NLS equation with an internal mode

Guillaume Rialland

We consider perturbations of the one-dimensional cubic Schrödinger equation, of the form $i \partial_{t} ψ + \partial_{x}^{2} ψ + ∣ ψ ∣^{2} ψ + g (∣ ψ ∣^{2}) ψ = 0$ . Under hypotheses on the func…

math.AP2023★ 2 cited

Asymptotic stability of solitary waves for the 1D near-cubic non-linear Schrödinger equation in the absence of internal modes

Guillaume Rialland

We consider perturbations of the one-dimensional cubic Schrödinger equation, under the form $i \partial_{t} ψ + \partial_{x}^{2} ψ + ∣ ψ ∣^{2} ψ - g (∣ ψ ∣^{2}) ψ = 0$ . Under hypotheses on the f…