The derivative NLS equation: global existence with solitons
TLDR
In this paper, the global existence result for the derivative NLS equation was extended to the case when the initial data set includes a finite number of solitons, by an application of the B\"{a}cklund transformation.Abstract:
We extend the global existence result for the derivative NLS equation to the case when the initial datum includes a finite number of solitons. This is achieved by an application of the B\"{a}cklund transformation that removes a finite number of zeros of the scattering coefficient. By means of this transformation, the Riemann--Hilbert problem for meromorphic functions can be formulated as the one for analytic functions, the solvability of which was obtained recently.read more
Citations
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Global well-posedness for the derivative nonlinear Schrödinger equation
Hajer Bahouri,Galina Perelman +1 more
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Finite gap integration of the derivative nonlinear Schrödinger equation: A Riemann–Hilbert method
Peng Zhao,Engui Fan +1 more
TL;DR: In this article, the Gerdjikov-Ivanov type derivative nonlinear Schrodinger equation was retrieved by using the algebro-geometric method and the Riemann-Hilbert method.
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Global existence for the derivative nonlinear Schrödinger equation with arbitrary spectral singularities
TL;DR: In this article, it was shown that the derivative nonlinear Schrodinger (DNLS) equation is globally well-posed in the weighted Sobolev space H 2,2(ℝ).
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Global well-posedness for the derivative non-linear Schrödinger equation
TL;DR: In this paper, the derivative nonlinear Schrodinger (DNLS) equation for general initial conditions in weighted Sobolev spaces that can support bright solitons (but exclude spectral singularities) was studied.
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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.
References
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Tables of Integrals, Series, and Products
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An exact solution for a derivative nonlinear Schrödinger equation
David J. Kaup,Alan C. Newell +1 more
TL;DR: In this paper, a method of solution for the derivative nonlinear Schrodinger equation is presented, where the appropriate inverse scattering problem is solved and the one-soliton solution is obtained, as well as the infinity of conservation laws.
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Scattering and inverse scattering for first order systems
Richard Beals,Ronald R. Coifman +1 more
TL;DR: In this article, the authors present resultats sur la theorie analytique des problemes de diffusion and de diffusion inverse for des systemes generalises AKNS. But they do not consider diffusion in general.
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The Darboux transformation of the derivative nonlinear Schr\"odinger equation
TL;DR: The n-fold Darboux transformation (DT) as mentioned in this paper is a 2-times2 matrix for the Kaup-Newell (KN) system and each element of this matrix is expressed by a ratio of $(n+1)times (n+ 1)$ determinant and $n\times n$ determinants of eigenfunctions.
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On the derivative nonlinear Schro¨dinger equation
Nakao Hayashi,Tohru Ozawa +1 more
TL;DR: In this article, the Cauchy problem for the derivative nonlinear Schrodinger equation was studied in the weighted Sobolev space and in the Schwartz class, and it was shown that there is a unique global existence of solutions to this problem.
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An exact solution for a derivative nonlinear Schrödinger equation
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