2024/12/11 by Eddye Bustamante, Bustamante, Eddye, José Jiménez Urrea +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Numerical methods for differential equations #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2412.08759
In this work we establish a dispersive blow-up result for the initial value problem (IVP) for the coupled Schrödinger-fifth order Korteweg-de Vries system . i ut+∂x2 u · amp;\hspace-2mm=αuv + γ|u|2 u, x∈\mathbb R, t∈\mathbb R,
∂t v + ∂x5 v + ∂x v2 · amp;\hspace-2mm=ε∂x |u|2, x∈\mathbb R, t∈\mathbb R,
u(x,0) · amp;\hspace-2mm= u0(x), v(x,0)=v0(x). \ To achieve this, we prove a local well-posedness result in Bourgain spaces of the type Xs+β,b× Ys,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.