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Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 4: Topics in Applied Analysis: special issue dedicated to Alexander Pankov on the occasion of his 65th birthday
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Articles

The asymptotic stability of solitons in the cubic NLS equation on the line

Scipio Cuccagna Department of Mathematics and Geosciences, University of Trieste, Trieste, 34127, Italy
&
Dmitry E. Pelinovsky Department of Mathematics and Statistics, McMaster University, Hamilton, Canada ON L8S 4K1Correspondence[email protected]
Pages 791-822 | Received 04 Feb 2013, Accepted 03 Nov 2013, Published online: 17 Dec 2013

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Andres Contreras, Dmitry E. Pelinovsky & Yusuke Shimabukuro. (2016) L2 orbital stability of Dirac solitons in the massive Thirring model. Communications in Partial Differential Equations 41:2, pages 227-255.
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Articles from other publishers (28)

Anran Liu & Engui Fan. (2024) On asymptotic stability of multi-solitons for the focusing modified Korteweg–de Vries equation. Physica D: Nonlinear Phenomena 459, pages 134046.
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Jonas Lührmann & Wilhelm Schlag. (2024) On codimension one stability of the soliton for the 1D focusing cubic Klein-Gordon equation. Communications of the American Mathematical Society 4:7, pages 230-356.
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Adilbek Kairzhan & Fabio Pusateri. (2023) Asymptotic stability near the soliton for quartic Klein–Gordon equation in 1D. Pure and Applied Analysis 5:4, pages 795-832.
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Qiaoyuan Cheng & Engui Fan. (2023) The Fokas-Lenells equation on the line: Global well-posedness with solitons. Journal of Differential Equations 366, pages 320-344.
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Andrey Gushin, Natalya Chertykovtseva, Svetlana Palevskaya, Olga Pavlova & Olga Gulenko. 2023. XV International Scientific Conference “INTERAGROMASH 2022”. XV International Scientific Conference “INTERAGROMASH 2022” 245 253 .
Yvan Martel. (2022) Asymptotic stability of solitary waves for the 1D cubic-quintic Schrödinger equation with no internal mode. Probability and Mathematical Physics 3:4, pages 839-867.
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Anran Liu & Engui Fan. (2022) The asymptotic stability of solitons for the focusing mKdV equation with weak weighted Sobolev initial data. Journal of Mathematical Physics 63:11.
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Gong Chen & Jiaqi Liu. (2022) Long-time asymptotics of the modified KdV equation in weighted Sobolev spaces. Forum of Mathematics, Sigma 10.
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Gong Chen & Jiaqi Liu. (2021) Soliton resolution for the focusing modified KdV equation. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 38:6, pages 2005-2071.
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Michał Kowalczyk, Yvan Martel, Claudio Muñoz & Hanne Van Den Bosch. (2021) A Sufficient Condition for Asymptotic Stability of Kinks in General (1+1)-Scalar Field Models. Annals of PDE 7:1.
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Scipio Cuccagna & Masaya Maeda. (2021) A survey on asymptotic stability of ground states of nonlinear Schrödinger equations II. Discrete & Continuous Dynamical Systems - S 14:5, pages 1693.
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Satoshi Masaki, Jason Murphy & Jun-ichi Segata. (2020) Stability of small solitary waves for the one-dimensional NLS with an attractive delta potential. Analysis & PDE 13:4, pages 1099-1128.
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Nabile Boussaïd & Andrew Comech. (2019) Spectral stability of small amplitude solitary waves of the Dirac equation with the Soler-type nonlinearity. Journal of Functional Analysis 277:12, pages 108289.
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Yuxin Lin, Yong Fang & Huanhe Dong. (2019) Prolongation Structures and -Soliton Solutions for a New Nonlinear Schrödinger-Type Equation via Riemann-Hilbert Approach . Mathematical Problems in Engineering 2019, pages 1-10.
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Dmitry E. Pelinovsky & Aaron Saalmann. 2019. Nonlinear Dispersive Partial Differential Equations and Inverse Scattering. Nonlinear Dispersive Partial Differential Equations and Inverse Scattering 497 528 .
Dmitry E Pelinovsky & Yusuke Shimabukuro. (2018) Existence of Global Solutions to the Derivative NLS Equation with the Inverse Scattering Transform Method. International Mathematics Research Notices 2018:18, pages 5663-5728.
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Pierre Germain, Fabio Pusateri & Frédéric Rousset. (2018) The nonlinear Schrödinger equation with a potential. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 35:6, pages 1477-1530.
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Jiaqi Liu, Peter A. Perry & Catherine Sulem. (2018) Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 35:1, pages 217-265.
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Michał Kowalczyk, Yvan Martel & Claudio Muñoz. (2017) On asymptotic stability of nonlinear waves. Séminaire Laurent Schwartz — EDP et applications, pages 1-27.
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Aaron Saalmann. (2017) Asymptotic stability of N-solitons in the cubic NLS equation. Journal of Hyperbolic Differential Equations 14:03, pages 455-485.
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Peter Perry. (2017) Inverse Scattering in 60 Minutes. Journées équations aux dérivées partielles, pages 1-17.
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Masaya Maeda. (2017) Existence and Asymptotic Stability of Quasi-Periodic Solutions of Discrete NLS with Potential. SIAM Journal on Mathematical Analysis 49:5, pages 3396-3426.
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Scipio Cuccagna & Robert Jenkins. (2016) On the Asymptotic Stability of $${N}$$ N -Soliton Solutions of the Defocusing Nonlinear Schrödinger Equation. Communications in Mathematical Physics 343:3, pages 921-969.
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Matt Coles & Stephen Gustafson. (2015) A degenerate edge bifurcation in the 1D linearized nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems 36:6, pages 2991-3009.
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C. Eugene Wayne & Michael I. WeinsteinMichael I. Weinstein. 2015. Dynamics of Partial Differential Equations. Dynamics of Partial Differential Equations 41 79 .
Stephan De Bièvre, François Genoud & Simona Rota Nodari. 2015. Nonlinear Optical and Atomic Systems. Nonlinear Optical and Atomic Systems 147 273 .
Stefan Le Coz & Tai-Peng Tsai. (2014) Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations. Nonlinearity 27:11, pages 2689-2709.
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Andres Contreras & Dmitry Pelinovsky. (2014) Stability of multi-solitons in the cubic NLS equation. Journal of Hyperbolic Differential Equations 11:02, pages 329-353.
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