The derivative NLS equation: global existence with solitons

2017/03/15 by Shimabukuro, Yusuke, Saalmann, Aaron, Pelinovsky, Dmitry E. · 3 citations
#Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1703.05277

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 Bäcklund 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.

Cited by

• Existence of global solutions to the Fokas-Lenells equation with arbitrary spectral singularities
• Semiclassical dynamics and coherent soliton ensembles in the derivative nonlinear Schrödinger equation with periodic initial conditions
• Well-posedness to nonlinear Schrödinger-Gerdjikov-Ivanon equation

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