Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg-de Vries equation

Abstract

In this article, we prove existence of a non-scattering solution, which is minimal in some sense, to the mass-subcritical generalized Korteweg-de Vries (gKdV) equation in the scale critical ^L^r space. We construct this solution by a concentration compactness argument. Then, key ingredients are a linear profile decomposition result adopted to ^L^r-framework and approximation of solutions to the gKdV equation which involves rapid linear oscillation by means of solutions to the nonlinear Schr"odinger equation.

74 pages

References in corpus (3)

• On well-posedness of generalized Korteweg-de Vries equation in scale critical ^L^r space
• Blow up for the critical gKdV equation III: exotic regimes
• On minimal non-scattering solution for focusing mass-subcritical nonlinear Schrödinger equation

Cited by in corpus (5)

• Two minimization problems on non-scattering solutions to mass-subcritical nonlinear Schrödinger equation
• Long range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity
• Modified scattering for the quadratic nonlinear Klein-Gordon equation in two dimensions
• Modified scattering for the Klein-Gordon equation with the critical nonlinearity in three dimensions
• Refinement of Strichartz estimate for Airy equation in non-diagonal case and its application