Global solution to the complex short pulse equation

Liju Yu; Jingjun Zhang; Liju Yu; Jingjun Zhang

doi:10.3934/era.2024220

Electronic Research Archive

2024, Volume 32, Issue 8: 4809-4827. doi: 10.3934/era.2024220

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Research article

Global solution to the complex short pulse equation

Liju Yu ^,,
Jingjun Zhang

Department of Mathematics, College of Data Science, Jiaxing University, Jiaxing 314001, China

Received: 09 March 2024 Revised: 23 July 2024 Accepted: 31 July 2024 Published: 08 August 2024

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.
- complex short pulse equation,
- conserved quantities,
- regularized solution,
- energy method,
- uniqueness
Citation: Liju Yu, Jingjun Zhang. Global solution to the complex short pulse equation[J]. Electronic Research Archive, 2024, 32(8): 4809-4827. doi: 10.3934/era.2024220

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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.

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