This work is devoted to investigating the local well-posedness for an integrable evolution equation and behaviors of its solutions, which possess blow-up criteria and persistence property. The existence and uniqueness of analytic solutions with analytic initial values are established. The solutions are analytic for both variables, globally in space and locally in time. The effects of coefficients λ and β on the solutions are given.

中文翻译：

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可积演化方程解的适定性和行为

这项工作致力于调查具有可爆标准和持久性的可积演化方程及其解的行为的局部适定性。建立了具有解析初始值的解析解的存在性和唯一性。该解决方案可以分析两个变量，分别是空间上的全局变量和时间上的局部变量。给出了系数λ和β对解的影响。