Stability of Multisolitons for the Derivative Nonlinear Schrödinger Equation
Stefan Le Coz,Yifei Wu +1 more
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This article is published in International Mathematics Research Notices.The article was published on 2017-02-26 and is currently open access. It has received 30 citations till now. The article focuses on the topics: Nonlinear Schrödinger equation & Derivative (chemistry).read more
Citations
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The derivative NLS equation: global existence with solitons
TL;DR: 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.
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Stability of the traveling waves for the derivative Schr\"odinger equation in the energy space
TL;DR: In this paper, the stability of the sum of two traveling waves for nonlinear Schrodinger equation with derivative (DNLS) is obtained in the energy space by Martel-Merle-Tsai's analytic approach.
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Stability of the traveling waves for the derivative Schrödinger equation in the energy space
TL;DR: In this paper, the stability of the sum of two traveling waves for nonlinear Schrodinger equation with derivative (DNLS) in the energy space has been studied under some technical assumptions on the speed of each traveling wave.
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Global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition in H12
TL;DR: In this article, the authors established the global well-posedness of the derivative nonlinear Schrodinger equation with periodic boundary condition in the Sobolev space, provided that the mass of initial data is less than 4π.
References
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Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media
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A relation between pointwise convergence of functions and convergence of functionals
TL;DR: In this article, it was shown that if f n is a sequence of uniformly L p-bounded functions on a measure space, and f n → f pointwise a, then lim for all 0 < p < ∞.
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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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Modulational Stability of Ground States of Nonlinear Schrödinger Equations
TL;DR: In this paper, the modulational stability of ground state solitary wave solutions of nonlinear Schrodinger equations relative to perturbations in the equation and initial data is studied.
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Integrability of Nonlinear Hamiltonian Systems by Inverse Scattering Method
TL;DR: In this paper, a simple and direct scheme is presented to test the integrability of nonlinear evolution equations by inverse scattering method, where the time part of the Lax equation needed for inverse scattering transform is identified with the linearized equation of the original nonlinear Hamiltonian system.