Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Dispersive blow-up for a coupled Schrödinger-fifth order KdV system (2412.08759v1)

Published 11 Dec 2024 in math.AP

Abstract: In this work we establish a dispersive blow-up result for the initial value problem (IVP) for the coupled Schr\"odinger-fifth order Korteweg-de Vries system \begin{align*} \left. \begin{array}{rl} i u_t+\partial_x2 u &\hspace{-2mm}=\alpha uv + \gamma |u|2 u, \quad x\in\mathbb R,\quad t\in\mathbb R,\ \partial_t v + \partial_x5 v + \partial_x v2&\hspace{-2mm}=\epsilon \partial_x |u|2, \quad x\in\mathbb R,\quad t\in\mathbb R,\ u(x,0)&\hspace{-2mm}= u_0(x), \quad v(x,0)=v_0(x). \end{array} \right} \end{align*} To achieve this, we prove a local well-posedness result in Bourgain spaces of the type $X{s+\beta,b}\times Y{s,b}$, along with a regularity property for the nonlinear part of the IVP solutions. This property enables the construction of initial data that leads to the dispersive blow-up phenomenon.

Summary

We haven't generated a summary for this paper yet.