Long time asymptotic behavior of the focusing nonlinear Schrödinger equation

By Michael M. Borghese, R. Jenkins, K. Mclaughlin. Annales de l'Institut Henri Poincare. Analyse non linéar, 2016

189 citations recorded by the source corpus.

We study the Cauchy problem for the focusing nonlinear Schrodinger (NLS) equation. Using the DBAR generalization of the nonlinear steepest descent method we compute the long time asymptotic expansion of the solution in any fixed space-time cone x_1 + v_1 t <= x <= x_2 + v_2 t with v_1 <= v_2 up to an (optimal) residual error of order O(t^(-3/4)). In each (x,t) cone the leading order term in this expansion is a multi-soliton whose parameters are modulated by soliton-soliton and soliton-radiation interactions as one moves through the cone. Our results only require that the initial data possess one L^2(R) moment and (weak) derivative and that it not generate any spectral singularities (embedded eigenvalues).

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/42d77b98ee76d91478e312e802fda96e7b1d471f

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In Mathematical Physics

1. R. Jenkins
2. Dmitry E. Pelinovsky
3. Yusuke Shimabukuro

In Statistical and Nonlinear Physics

1. Catherine Sulem
2. Peter Perry
3. Jiaqi Liu
4. R. Jenkins
5. Dmitry E. Pelinovsky
6. Yusuke Shimabukuro
7. F. Merle

Citations in the corpus

• Soliton Resolution for the Derivative Nonlinear Schrödinger Equation (2017, methodology): “6 are given in Sections 2, 3, and 4, using the steepest descent method of Deift and Zhou [7], the later approach of McLaughlin-Miller [24] and Dieng-McLaughlin [9], and the recent work of Borghese, Jenkins and McLaughlin [1] on the focusing cubic NLS which shows how to treat a problem with discrete ”