Long-time Asymptotic for the Derivative Nonlinear Schrodinger Equation with Step-like Initial Value
被引:60
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作者:
Xu, Jian
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Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R ChinaFudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
Xu, Jian
[1
]
Fan, Engui
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Fudan Univ, Inst Math, Sch Math Sci, Shanghai 200433, Peoples R China
Fudan Univ, Key Lab Math Nonlinear Sci, Shanghai 200433, Peoples R ChinaFudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
Fan, Engui
[2
,3
]
Chen, Yong
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E China Normal Univ, Shanghai Key Lab Trustworthy Comp, Shanghai 200062, Peoples R ChinaFudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
Chen, Yong
[4
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机构:
[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
[2] Fudan Univ, Inst Math, Sch Math Sci, Shanghai 200433, Peoples R China
[3] Fudan Univ, Key Lab Math Nonlinear Sci, Shanghai 200433, Peoples R China
[4] E China Normal Univ, Shanghai Key Lab Trustworthy Comp, Shanghai 200062, Peoples R China
We study long-time asymptotics of the solution to the Cauchy problem for the Gerdjikov-Ivanov type derivative nonlinear Schrodinger equation iq(t) + q(xx) - iq(2)(q) over bar (x) + 1/2 vertical bar q vertical bar(4)q = 0 with step-like initial data q(x, 0) = 0 for x <= 0 and q(x, 0) = Ae(-2i Bx) for x > 0, where A > 0 and B is an element of R are constants. We show that there are three regions in the half-plane {(x, t)| - infinity < x < infinity, t > 0}, on which the asymptotics has qualitatively different forms: a slowly decaying self-similar wave of Zakharov-Manakov type for , a plane wave region: x < -4t (B + root 2A(2) (B + A(2)/4)), an elliptic region: -4t (B + root 2A(2) (B + A(2)/4)) < x < -4tB. Our main tools include asymptotic analysis, matrix Riemann-Hilbert problem and Deift-Zhou steepest descent method.
机构:
Shanghai Polytech Univ, Dept Math, Shanghai 201209, Peoples R ChinaShanghai Polytech Univ, Dept Math, Shanghai 201209, Peoples R China
Wen, Lili
Chen, Yong
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机构:
East China Normal Univ, Sch Math Sci, Shanghai Key Lab Pure Math & Math Practice, Shanghai 200241, Peoples R China
Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R ChinaShanghai Polytech Univ, Dept Math, Shanghai 201209, Peoples R China
Chen, Yong
Xu, Jian
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机构:
Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R ChinaShanghai Polytech Univ, Dept Math, Shanghai 201209, Peoples R China