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. Letters in Mathematical Physics Springer Journals

The short pulse equation by a Riemann–Hilbert approach

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Springer Netherlands
Copyright © 2017 by Springer Science+Business Media Dordrecht
Physics; Theoretical, Mathematical and Computational Physics; Complex Systems; Geometry; Group Theory and Generalizations
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