We establish local and global existence of periodic solutions for KdV type equations, employing Fourier series and a fixed point argument. We also investigate the polynomial growth of the solutions.
"Existence and polynomial growth of periodic solutions to KdV-type equations." Hokkaido Math. J. 34 (3) 629 - 654, October 2005. https://doi.org/10.14492/hokmj/1285766289