In this note, we review stability properties in energy spaces of three important nonlinear
Schrödinger breathers: Peregrine, Kuznetsov-Ma, and Akhmediev. More precisely, we show …

In this paper, we study the long-time dynamics and stability properties of the sine-Gordon
equation $$ f_ {tt}-f_ {xx}+\sin f= 0. $$ Firstly, we use the nonlinear steepest descent for …

We study the long-time asymptotic behavior of the solution q(x,t), x∈R, t∈R^+, of the
modified Korteweg--de Vries equation (MKdV) q_t+6q^2q_x+q_xxx=0 with step-like initial …

Based on the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann–
Hilbert problems and the Dbar approach, the long‐time asymptotic behavior of solutions to …

We consider the logarithmic Schr\" odinger equation in the focusing regime. For this
equation, Gaussian initial data remains Gaussian. In particular, the Gausson-a time …

In this work, the $\overline {\partial} $ steepest descent method is employed to investigate
the soliton resolution for the Hirota equation with the initial value belong to weighted …

We establish the nonlinear stability of N-soliton solutions of the modified Korteweg–de Vries
(mKdV) equation. The N-soliton solutions are global solutions of mKdV behaving at (positive …

We prove a local well-posedness result for the modified Korteweg–de Vries equation in a
critical space designed so that is contains self-similar solutions. As a consequence, we can …

We consider solutions of the generalized Korteweg-de Vries equations (gKdV) which are
non dispersive in some sense and which remain close to multi-solitons. We show that these …

We consider the cubic Nonlinear Schrödinger Equation (NLS) and the Modified Korteweg-
de-Vries Equation (mKdV) in the one-dimensional, focusing case. For the mKdV, we also …