On the Local Well-posedness for Some Systems of Coupled Kdv Equations

Using the theory developed by Kenig, Ponce, and Vega, we prove that the Hirota-Satsuma system is locally well-posed in Sobolev spaces H(R)× H(R) for 3/4 < s ≤ 1. We introduce some Bourgain-type spaces X s,b for a 6= 0, s, b ∈ R to obtain local well-posedness for the Gear-Grimshaw system in H(R)×H(R) for s > −3/4, by establishing new mixed-bilinear estimates… CONTINUE READING