一类二元可积系统的适定性问题研究

Well-Posedness for a New Two-Component Integrable System

中文关键词:  Besov空间  二元可积系统  适定性.

英文关键词:Besov space  two-component integrable system  local well-posedness.

中文摘要:

      我们主要考虑一类新的二元可积系统.该系统不仅具有双哈密尔顿结构,满足无限守恒律,且关于其Lax对可积.本文我们主要确立了在Besov空间($s>\max\{2+\frac{1}{p},\frac{5}{2}\}$)范围内该系统的局部适定性.

英文摘要:

      In this paper, we consider a new two-component integrable system with cubic nonlinearity, which can be deduced by a curve flow and it is integrable with its Lax pair, bi-Hamiltonian structure, and infinitely many conservation laws. We mainly establish the local well-posedness of this system in a range of the Besov spaces $B^s_{p,r}$ with $s>\max\{2+\frac{1}{p},\frac{5}{2}\}$.