Global Cauchy problems for the nonlocal (derivative) NLS in Eσs

[1]  Baoxiang Wang,et al.  Complex valued semi-linear heat equations in super-critical spaces $$E^s_\sigma $$ , 2022, Mathematische Annalen.

[2]  M. Russo Local and nonlocal solitons in a coupled real system of Landau–Lifshitz equations , 2021 .

[3]  D. Shepelsky,et al.  Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data , 2021, Journal of Differential Equations.

[4]  H. Feichtinger,et al.  Navier-Stokes equation in super-critical spacesEp,qs , 2020 .

[5]  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.

[6]  Shoufeng Shen,et al.  Solutions and connections of nonlocal derivative nonlinear Schrödinger equations , 2018, Nonlinear Dynamics.

[7]  Mark J. Ablowitz,et al.  General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions , 2017, Nonlinearity.

[8]  D. Shepelsky,et al.  Long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation , 2017, Journal of Mathematical Physics.

[9]  Asli Pekcan,et al.  Nonlocal Nonlinear Schr\"odinger Equations and Their Soliton Solutions , 2017, 1707.07610.

[10]  Zi-Xiang Zhou,et al.  Darboux transformations and global solutions for a nonlocal derivative nonlinear Schrödinger equation , 2016, Commun. Nonlinear Sci. Numer. Simul..

[11]  Franccois Genoud Instability of an integrable nonlocal NLS , 2016, 1612.03139.

[12]  T. Gadzhimuradov,et al.  Towards a gauge-equivalent magnetic structure of the nonlocal nonlinear Schrödinger equation , 2016 .

[13]  Tadahiro Oh A remark on norm inflation with general initial data for the cubic nonlinear Schr\"odinger equations in negative Sobolev spaces , 2015, 1509.08143.

[14]  V. Gerdjikov,et al.  Complete integrability of Nonlocal Nonlinear Schr\"odinger equation , 2015, 1510.00480.

[15]  Shaoming Guo On the 1D Cubic Nonlinear Schrödinger Equation in an Almost Critical Space , 2014, 1411.0503.

[16]  M. Ablowitz,et al.  Integrable nonlocal nonlinear Schrödinger equation. , 2013, Physical review letters.

[17]  Dong Li Global well-posedness of hedgehog solutions for the (3+1) Skyrme model , 2012, Duke Mathematical Journal.

[18]  Herbert Koch,et al.  Well-posedness and scattering for the KP-II equation in a critical space , 2007, 0708.2011.

[19]  Gino Biondini,et al.  Inverse scattering transform for the integrable discrete nonlinear Schrödinger equation with nonvanishing boundary conditions , 2007 .

[20]  D. Tataru,et al.  Dispersive estimates for principally normal pseudodifferential operators , 2004, math/0401234.

[21]  Nakao Hayashi,et al.  Finite energy solutions of nonlinear Schrdinger equations of derivative type , 1994 .

[22]  Y. Tsutsumi L$^2$-Solutions for Nonlinear Schrodinger Equations and Nonlinear Groups , 1985 .

[23]  Baoxiang Wang,et al.  Local well-posedness for the derivative nonlinear Schrödinger equation with $ L^2 $-subcritical data , 2021, Discrete & Continuous Dynamical Systems.