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Preprints, Working Papers, ... Year : 2016

THE SHORT PULSE EQUATION BY A RIEMANN-HILBERT APPROACH

Abstract

We develop a Riemann-Hilbert approach to the inverse scattering transform method for the short pulse (SP) equation u_xt = u + 1/6 (u^3)_xx with zero boundary conditions (as |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 long-time behavior of the solution as well as for retrieving the soliton solutions. Finally, the analysis of the long-time behavior allows us to formulate, in spectral terms, a sufficient condition for the wave breaking.
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hal-03662513 , version 1 (09-05-2022)

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Anne Boutet de Monvel, Dmitry Shepelsky, Lech Zielinski. THE SHORT PULSE EQUATION BY A RIEMANN-HILBERT APPROACH. 2016. ⟨hal-03662513⟩
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