Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
In a recent paper, Kenig, Ponce and Vega study the low regularity behavior of the focusing nonlinear Schrödinger (NLS), focusing modified Korteweg-de Vries (mKdV), and complex Korteweg-de Vries (KdV) equations. Using soliton and breather solutions, they demonstrate the lack of local well-posedness for these equations below their respective endpoint regularities. …