Construction of dynamics with strongly interacting for non-linear dispersive PDE (Partial differential equation).

Abstract : This thesis deals with long time dynamics of soliton solutions for nonlinear dispersive partial differential equation (PDE). Through typical examples of such equations, the nonlinear Schrödinger equation (NLS), the generalized Korteweg-de Vries equation (gKdV) and the coupled system of Schrödinger, we study the behavior of solutions, when time goes to infinity, towards sums of solitons (multi-solitons). First, we show that in the symmetric setting, with strong interactions, the behavior of logarithmic separation in time between solitons is universal in both subcritical and supercritical case. Next, adapting previous techniques to (gKdV) equation, we prove a similar result of existence of multi-solitons with logarithmic relative distance; for (gKdV), the solitons are repulsive in the subcritical case and attractive in the supercritical case. Finally, we identify a new logarithmic regime where the solitons are non-symmetric for the non-integrable coupled system of Schrödinger; such solution does not exist in the integrable case for the system and for (NLS).
Document type :
Theses
Complete list of metadatas

Cited literature [151 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-02168161
Contributor : Abes Star <>
Submitted on : Friday, June 28, 2019 - 2:28:08 PM
Last modification on : Monday, July 8, 2019 - 2:59:19 PM

File

85575_NGUYEN_2019_archivage.pd...
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-02168161, version 1

Citation

Tien Vinh Nguyen. Construction of dynamics with strongly interacting for non-linear dispersive PDE (Partial differential equation).. Analysis of PDEs [math.AP]. Université Paris-Saclay, 2019. English. ⟨NNT : 2019SACLX024⟩. ⟨tel-02168161⟩

Share

Metrics

Record views

305

Files downloads

65