اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدLong time asymptotic for the Wadati-Konno-Ichikawa equation with finite density initial data
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In this work, we investigate the Cauchy problem of the Wadati-Konno-Ichikawa (WKI) equation with finite density initial data. Employing the $bar{partial}$-generalization of Deift-Zhou nonlinear steepest descent method, we derive the long time asymptotic behavior of the solution $q(x,t)$ in space-time soliton region. Based on the resulting asymptotic behavior, the asymptotic approximation of the WKI equation is characterized with the soliton term confirmed by $N(I)$-soliton on discrete spectrum and the $t^{-frac{1}{2}}$ leading order term on continuous spectrum with residual error up to $O(t^{-frac{3}{4}})$. Our results also confirm the soliton resolution conjecture for the WKI equation with finite density initial data.
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