A Note on the Critical Length Phenomenon for the Korteweg-de Vries Equation

Over the past 25 years, the critical length phenomenon for the Korteweg- de Vries (KdV) equation has been challenging. After Rosier’s pioneering work in 1997, some authors tried to find boundary conditions that would guarantee the characterization of the critical set explicitly. In this chapter, we will give some results in this sense and present new results that complement previous results in the literature for the KdV equation considering Neuman boundary conditions.