ON THE MASS-CRITICAL GENERALIZED KDV EQUATION

Abstract

We consider the mass-critical generalized Korteweg-de Vries equation (partial derivative(t) + partial derivative(xxx))u = +/-partial derivative(x)(u(5)) for real-valued functions u(t, x). We prove that if the global well-posedness and scattering conjecture for this equation failed, then, conditional on a positive answer to the global well-posedness and scattering conjecture for the mass-critical nonlinear Schrodinger equation (-i partial derivative(t) + partial derivative(xx))u =+/-(vertical bar u vertical bar(4)u), there exists a minimal-mass blowup solution to the mass-critical generalized KdV equation which is almost periodic modulo the symmetries of the equation. Moreover, we can guarantee that this minimal-mass blowup solution is either a self-similar solution, a soliton-like solution, or a double high-to-low frequency cascade solution.