Long time asymptotic behavior for the nonlocal nonlinear Schr\"odinger equation with weighted Sobolev initial data
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[1] M. Segev,et al. Theory of Self-Trapped Spatially Incoherent Light Beams , 1997 .
[2] C. Bender,et al. Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry , 1997, physics/9712001.
[3] P. Perry,et al. Soliton Resolution for the Derivative Nonlinear Schrödinger Equation , 2017, 1710.03819.
[4] M. Ablowitz,et al. Integrable space-time shifted nonlocal nonlinear equations , 2021 .
[5] K. Mclaughlin,et al. Long time asymptotic behavior of the focusing nonlinear Schrödinger equation , 2016, Annales de l'Institut Henri Poincaré C, Analyse non linéaire.
[6] P. Miller,et al. The Steepest Descent Method for Orthogonal Polynomials on the Real Line with Varying Weights , 2008, 0805.1980.
[7] Jianke Yang,et al. Nonlinear waves in PT -symmetric systems , 2016, 1603.06826.
[8] Asli Pekcan,et al. Nonlocal Nonlinear Schr\"odinger Equations and Their Soliton Solutions , 2017, 1707.07610.
[9] E. Fan,et al. Soliton resolution for the short-pulse equation , 2020, 2005.12208.
[10] M. Znojil. What is PT symmetry , 2001 .
[11] M. Segev,et al. Observation of parity–time symmetry in optics , 2010 .
[12] M. Ablowitz,et al. Integrable nonlocal nonlinear Schrödinger equation. , 2013, Physical review letters.
[13] D. Shepelsky,et al. Long-Time Asymptotics for the Integrable Nonlocal Focusing Nonlinear Schrödinger Equation for a Family of Step-Like Initial Data , 2019, Communications in Mathematical Physics.
[14] P. Deift,et al. A steepest descent method for oscillatory Riemann–Hilbert problems. Asymptotics for the MKdV equation , 1993 .
[15] PT-symmetry, indefinite metric, and nonlinear quantum mechanics , 2017 .
[16] Z. Musslimani,et al. Beam dynamics in PT symmetric optical lattices. , 2008, Physical review letters.
[17] D. Shepelsky,et al. Long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation , 2017, Journal of Mathematical Physics.
[18] T. Gadzhimuradov,et al. Towards a gauge-equivalent magnetic structure of the nonlocal nonlinear Schrödinger equation , 2016 .
[19] M. Ablowitz,et al. Discrete nonlocal nonlinear Schrödinger systems: Integrability, inverse scattering and solitons , 2020, Nonlinearity.
[20] P. Alam. ‘K’ , 2021, Composites Engineering.
[21] P. Deift,et al. A steepest descent method for oscillatory Riemann–Hilbert problems. Asymptotics for the MKdV equation , 1992, math/9201261.
[22] M. Ablowitz,et al. Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation , 2016 .
[23] B. Malomed,et al. Stable dark solitons in PT-symmetric dual-core waveguides , 2012, 1211.3746.
[24] D. Shepelsky,et al. Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data , 2021 .
[25] U. Peschel,et al. Parity–time synthetic photonic lattices , 2012, Nature.
[26] The ∂ Steepest Descent Method and the Asymptotic Behavior of Polynomials Orthogonal on the Unit Circle with Fixed and Exponentially Varying Nonanalytic Weights , 2004, math/0406484.
[27] R. Morandotti,et al. Observation of PT-symmetry breaking in complex optical potentials. , 2009, Physical review letters.