Kavli Affiliate: Ran Wang
| First 5 Authors: Nan Liu, Ran Wang, , ,
| Summary:
We address the long-time asymptotics of the solution to the Cauchy problem of
ccSP (coupled complex short pulse) equation on the line for decaying initial
data that can support solitons. The ccSP system describes ultra-short pulse
propagation in optical fibers, which is a completely integrable system and
posses a $4times4$ matrix Wadati–Konno–Ichikawa type Lax pair. Based on the
$bar{partial}$-generalization of the Deift–Zhou steepest descent method, we
obtain the long-time asymptotic approximations of the solution in two kinds of
space-time regions under a new scale $(zeta,t)$. The solution of the ccSP
equation decays as a speed of $O(t^{-1})$ in the region $zeta/t>varepsilon$
with any $varepsilon>0$; while in the region $zeta/t<-varepsilon$, the
solution is depicted by the form of a multi-self-symmetric soliton/composite
breather and $t^{-1/2}$ order term arises from self-symmetric soliton/composite
breather-radiation interactions as well as an residual error order $O(t^{-1}ln
t)$.
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