Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation (Q2581838)

The authors consider the initial value problem for a generalized Korteweg-de Vries equation in \(u=u(x,t)\), \(u_t+u_{xxx}+u^pu_x=0\), where \(p\) is a positive integer (\(p=1\) gives the Korteweg-de Vries equation itself, and \(p=2\) the modified Korteweg-de Vries equation, both completely integrable). In fact, they consider the case of complex-valued solutions (so the initial data will be drawn from a suitable class of analytic functions). The focus is on studying the asymptotics of the width of the strip of analyticity for large time \(t\). They obtain algebraically decreasing time-asymptotics for this width.