Global well-posedness of the short-pulse and sine-Gordon equations in energy space

We prove global well-posedness of the short-pulse equation with small initial data in Sobolev space $H^2$. Our analysis relies on local well-posedness results of Sch"afer & Wayne, the correspondence of the short-pulse equation to the sine-Gordon equation in characteristic coordinates, and a number of conserved quantities of the short-pulse equation. We also prove local and global well-posedness of the sine-Gordon equation in an appropriate function space.

💡 Research Summary

The paper addresses the global well‑posedness problem for two closely related nonlinear wave equations: the short‑pulse equation (SPE) and the sine‑Gordon equation (SGE). The SPE, originally derived as a model for ultra‑short optical pulses, reads
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