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Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation. (English) Zbl 1095.35039
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.

##### MSC:
 35Q53 KdV equations (Korteweg-de Vries equations) 35B40 Asymptotic behavior of solutions to PDEs
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##### References:
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