Long time behavior of the fractional Korteweg-de Vries equation with cubic nonlinearity

Abstract

We prove global existence and modified scattering for the solutions of the Cauchy problem to the fractional Korteweg-de Vries equation with cubic nonlinearity for small, smooth and localized initial data.

References in corpus (3)

• A numerical approach to Blow-up issues for dispersive perturbations of Burgers' equation
• Wave breaking for the Whitham equation with fractional dispersion
• Enhanced existence time of solutions to the fractional Korteweg-de Vries equation

Cited by in corpus (5)

• The wave breaking for Whitham-type equations revisited
• Global dynamics of small solutions to the modified fractional Korteweg-de Vries and nonlinear Schrödinger equations
• On persistence properties in weighted spaces for solutions of the fractional Korteweg-de Vries equation
• Wave breaking for the generalized Fornberg-Whitham equation
• Global dynamics of the generalized fifth-order KdV equation with critical nonlinearity