期刊
LETTERS IN MATHEMATICAL PHYSICS
卷 107, 期 7, 页码 1345-1373出版社
SPRINGER
DOI: 10.1007/s11005-017-0945-z
关键词
Short pulse equation; Short wave equation; Camassa-Holm-type equation; Inverse scattering transform; Riemann-Hilbert problem
We develop a Riemann-Hilbert approach to the inverse scattering transform method for the short pulse (SP) equation with zero boundary conditions (as ). This approach is directly applied to a Lax pair for the SP equation. It allows us to give a parametric representation of the solution to the Cauchy problem. This representation is then used for studying the longtime behavior of the solution as well as for retrieving the soliton solutions. Finally, the analysis of the longtime behavior allows us to formulate, in spectral terms, a sufficient condition for the wave breaking.
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