AI 中文总结
本文研究带概周期初值的散焦型mKdV方程的柯西问题，针对满足特定条件的初值证明其存在时空概周期的唯一局部有界解，相关结果适用于特定准周期初值。
AI 中文摘要
我们研究带有概周期初值的散焦型mKdV方程的柯西问题。若初值对应满足谱上特定Craig型条件的无反射Dirac算子，我们证明该柯西问题存在时空上概周期的解，且这是在合适意义下局部有界的唯一解。特别地，该结果适用于带有丢番图频率的小解析准周期初值。
英文摘要
We study the Cauchy problem for the defocusing mKdV equation with almost periodic initial data. If the initial data corresponds to a reflectionless Dirac operator which satisfies certain Craig-type conditions on the spectrum, we prove that the Cauchy problem has solution that is almost periodic in spacetime, and that this is the only solution which is locally bounded in a suitable sense. In particular, the result applies to small analytic quasiperiodic initial data with Diophantine frequencies.
Comments17 pages, comments are welcome!
