In this paper, we consider small perturbations of the KdV-mKdV equation
ut=-uxxx + 6uux + 6u2ux
on the real line with periodic boundary conditions. It is shown that the above equation admits a Cantor family of small amplitude quasi-periodic solutions under such perturbations. The proof is based on an abstract infinite dimensional KAM theorem.
Wenyan CUI
,
Lufang MI
,
Li YIN
. KAM TORI FOR DEFOCUSING KDV-MKDV EQUATION[J]. Acta mathematica scientia, Series B, 2019
, 39(1)
: 243
-258
.
DOI: 10.1007/s10473-019-0119-4
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