Global solution to the complex short pulse equation

Abstract

This paper deals with global well-posedness of the solution to the complex short pulse equation. We first use regularized technology and the approximation argument to prove the local existence and uniqueness of this equation. Then, based on conserved quantities and energy analysis, we show that the solution can be extended globally in time for suitably small initial data.

Keywords

• complex short pulse equation
• conserved quantities
• regularized solution
• energy method
• uniqueness