The short pulse equation by a Riemann–Hilbert approach

The short pulse equation by a Riemann–Hilbert approach We develop a Riemann–Hilbert approach to the inverse scattering transform method for the short pulse (SP) equation $$\begin{aligned} u_{xt}=u+\tfrac{1}{6}(u^3)_{xx} \end{aligned}$$ u x t = u + 1 6 ( u 3 ) x x with zero boundary conditions (as $$|x|\rightarrow \infty $$ | x | → ∞ ). 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Letters in Mathematical Physics Springer Journals

The short pulse equation by a Riemann–Hilbert approach

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Publisher
Springer Netherlands
Copyright
Copyright © 2017 by Springer Science+Business Media Dordrecht
Subject
Physics; Theoretical, Mathematical and Computational Physics; Complex Systems; Geometry; Group Theory and Generalizations
ISSN
0377-9017
eISSN
1573-0530
D.O.I.
10.1007/s11005-017-0945-z
Publisher site
See Article on Publisher Site

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