D. Pelinovsky and A. Sakovich
Global well-posedness of the short-pulse and sine-Gordon equations in energy space
Communications in PDE 35, 613-629 (2010)
We prove global well-posedness of the short-pulse equation with small initial data in
Sobolev space Hs for an integer s >= 2. Our analysis relies
on local well-posedness results of Schafer & Wayne (2004),
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 vector space.
Short-pulse equation, sine-Gordon equation in characterstic coordinates,
well-posedness, conserved quantities, wave breaking.