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The Sasa-Satsuma equation with high-order discrete spectra in space-time solitonic regions:soliton resolution via the mixed■-Riemann-Hilbert problem

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Communications in Theoretical Physics 2024年第6期76卷 13-25页

作者： Minghe Zhang Zhenya Yan KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we investigate the Cauchy problem of the Sasa-Satsuma(SS)equation with initial data belonging to the Schwartz *** SS equation is one of the integrable higher-order extensions of the nonlinear Schrödinger equation and admits a 3×3 Lax *** the aid of the■nonlinear steepest descent method of the mixed■-Riemann-Hilbert problem,we give the soliton resolution and long-time asymptotics for the Cauchy problem of the SS equation with the existence of second-order discrete spectra in the space-time solitonic regions.

关键词： Sasa-Satsuma equation inverse scattering ■-Riemann-Hilbert problem ■steepest descent method soliton resolution

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Long-time Asymptotic Behavior for the Derivative Schrödinger Equation with Finite Density Type Initial Data

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Chinese Annals of Mathematics,Series B 2022年第6期43卷 893-948页

作者： Yiling YANG Engui FAN School of Mathematical Sciences Fudan UniversityShanghai 200433China

In this paper,the authors apply■steepest descent method to study the Cauchy problem for the derivative nonlinear Schrödinger equation with finite density type initial data iqt+qxx+1(lq|^(2)q)_(x)=0,q(x,0)=q0(x),where lim x→±∞ qo(x)=g0(x)=q±and|q±|=*** on the spectral analysis of the Lax pair,they express the solution of the derivative Schrödinger equation in terms of solutions of a Riemann-Hilbert *** compute the long time asymptotic expansion of the solution in differeit space-time *** the regionζ=x/t with|ζ+2|1,the long time asymptotic is given by q(x,t)=t(∞)^(-2)q^(r)Λ(x,t)-t^(-1/2)if11+O(t^(-3/4)) in which the leading term is N(I)solitons,the second t^(-1/2)order term is soliton-radiation interactions and the third term is a residual error from a■*** results are verification of the soliton resolution conjectuore for the derivative Schrödinger *** their case of finite density type initial data,the phase functionθ(z)is more complicated that in finite mass initial ***,two triangular decompositions of the jump matrix are used to open jump lines on the whole real axis and imaginary axis,respectively.

关键词： Derivative Schrödinger equation Riemann-Hilbert problem ■steepest descent method Long-time asymptotics Soliton resolution Asymptotic stability

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