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Global well-posedness for the derivative nonlinear Schrödinger equation
Hajer Bahouri,Galina Perelman +1 more
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The article was published on 2020-12-03 and is currently open access. It has received 39 citations till now. The article focuses on the topics: Nonlinear system & Derivative (finance).read more
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Global well-posedness for the derivative nonlinear Schr\"odinger equation.
Hajer Bahouri,Galina Perelman +1 more
TL;DR: In this paper, it was shown that the derivative nonlinear Schrodinger equation is globally well-posed for general Cauchy data in the weighted Sobolev space, and furthermore the norm of the solutions remains globally bounded in time.
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Modulational instability of periodic standing waves in the derivative NLS equation
TL;DR: All periodic standing waves are classified in terms of eight eigenvalues of the Kaup-Newell spectral problem located at the end points of the spectral bands outside the real line by a newly developed algebraic method with two eigen values.
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Modulational Instability of Periodic Standing Waves in the Derivative NLS Equation
TL;DR: In this paper, the periodic standing waves in the derivative nonlinear Schrodinger (DNLS) equation arising in plasma physics were classified in terms of eight eigenvalues of the Kaup-Newell spectral problem located at the end points of the spectral bands outside the real line.
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A priori estimates for the derivative nonlinear Schrödinger equation
Friedrich Klaus,Robert Schippa +1 more
TL;DR: In this article, low regularity a priori estimates for the derivative nonlinear Schrodinger equation in Besov spaces with positive regularity index conditional upon small $L^2$ -norm were obtained.
References
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Book
Solitons and the Inverse Scattering Transform
Mark J. Ablowitz,Harvey Segur +1 more
TL;DR: In this paper, the authors developed the theory of the inverse scattering transform (IST) for ocean wave evolution, which can be solved exactly by the soliton solution of the Korteweg-deVries equation.
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Trace ideals and their applications
TL;DR: In this paper, Calkin's theory of operator ideals and symmetrically normed ideals convergence theorems for trace, determinant, and Lidskii's theorem are discussed.
Journal ArticleDOI
On the modulational instability of hydromagnetic waves parallel to the magnetic field
TL;DR: In this paper, the stability of circularly polarized waves of finite amplitude propagating parallel to the magnetic field is studied. And the authors show that finite amplitude always promotes stability, while amplitude dependent stability conditions for long waves, previously obtained by the author, are confirmed.
Journal ArticleDOI
A Refined Global Well-Posedness Result for Schrödinger Equations with Derivative
TL;DR: In this paper, it was shown that the one-dimensional Schrodinger equation with derivative in the nonlinear term is globally well-posed in Hs for data small in L2.
Journal ArticleDOI
On the Absolutely Continuous Spectrum of One-Dimensional Schrödinger Operators with Square Summable Potentials
Percy Deift,Rowan Killip +1 more
TL;DR: For continuous and discrete one-dimensional Schrodinger operators with square summable potentials, the absolutely continuous part of the spectrum is essentially supported by [0,∞) and [−2,2] as mentioned in this paper.
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