[1]
|
Zhu, S., Zhang, J. and Yang, H. (2010) Limiting Profile of the Blow-Up Solutions for the Fourth-Order Nonlinear Schro¨dinger Equation. Dynamics of Partial Differential Equations, 7, 187-205. https://doi.org/10.4310/DPDE.2010.v7.n2.a4
|
[2]
|
Guo, Q. (2016) Scattering for the Focusing L2-Supercritical and H˙ 2-Subcritical Biharmonic NLS Equations. Communications in Partial Differential Equations, 41, 185-207. https://doi.org/10.1080/03605302.2015.1116556
|
[3]
|
Li, Y., Wu, Y. and Xu, G. (2011) Global Well-Posedness for the Mass-Critical Nonlinear Schro¨dinger Equation on T. Journal of Differential Equations, 250, 2715-2736. https://doi.org/10.1016/j.jde.2011.01.025
|
[4]
|
Li, Y., Wu, Y. and Xu, G. (2011) Low Regularity Global Solutions for the Focusing Mass- Critical NLS in R. SIAM Journal on Mathematical Analysis, 43, 322-340. https://doi.org/10.1137/090774537
|
[5]
|
Wu, Y. (2013) Global Well-Posedness of the Derivative Nonlinear Schro¨dinger Equations in Energy Space. Analysis & PDE, 6, 1989-2002. https://doi.org/10.2140/apde.2013.6.1989
|
[6]
|
Liu, X., Simpson, G. and Sulem, C. (2013) Stability of Solitary Waves for a Generalized Derivative Nonlinear Schro¨dinger Equation. Journal of Nonlinear Science, 23, 557-583. https://doi.org/10.1007/s00332-012-9161-2
|
[7]
|
Wu, Y. (2015) Global Well-Posedness on the Derivative Nonlinear Schro¨dinger Equation. Anal- ysis & PDE, 8, 1101-1113. https://doi.org/10.2140/apde.2015.8.1101
|
[8]
|
Ning, C., Ohta, M. and Wu, Y. (2017) Instability of Solitary Wave Solutions for Derivative Nonlinear Schro¨dinger Equation in Endpoint Case. Journal of Differential Equations, 262, 1671-1689. https://doi.org/10.1016/j.jde.2016.10.020
|
[9]
|
Le Coz, S. and Wu, Y. (2018) Stability of Multi-Solitons for the Derivative Nonlinear Schro¨dinger Equation. International Mathematics Research Notices, No. 13, 4120-4170. https://doi.org/10.1093/imrn/rnx013
|
[10]
|
Ning, C. (2020) Instability of Solitary Wave Solutions for Derivative Nonlinear Schr¨odinger Equation in Borderline Case. Nonlinear Analysis, 192, Article ID: 111665. https://doi.org/10.1016/j.na.2019.111665
|
[11]
|
Feng, B. and Zhu, S. (2021) Stability and Instability of Standing Waves for the Fractional Nonlinear Schro¨dinger Equations. Journal of Differential Equations, 292, 287-324. https://doi.org/10.1016/j.jde.2021.05.007
|
[12]
|
Court`es, C., Lagouti`ere, F. and Rousset, F. (2020) Error Estimates of Finite Difference Schemes for the Korteweg-de Vries Equation. IMA Journal of Numerical Analysis, 40, 628-685. https://doi.org/10.1093/imanum/dry082
|
[13]
|
Holden, H., Koley, U. and Risebro, N. (2014) Convergence of a Fully Discrete Finite Difference Scheme for the Korteweg-de Vries Equation. IMA Journal of Numerical Analysis, 35, 1047- 1077. https://doi.org/10.1093/imanum/dru040
|
[14]
|
Aksan, E. and O¨ zde¸s, A. (2006) Numerical Solution of Korteweg-de Vries Equation by Galerkin B-Spline Finite Element Method. Applied Mathematics and Computation, 175, 1256-1265. https://doi.org/10.1016/j.amc.2005.08.038
|
[15]
|
Dutta, R., Koley, U. and Risebro, N.H. (2015) Convergence of a Higher Order Scheme for the Korteweg-de Vries Equation. SIAM Journal on Numerical Analysis, 53, 1963-1983. https://doi.org/10.1137/140982532
|
[16]
|
Holden, H., Karlsen, K.H., Risebro, N.H. and Tang, T. (2011) Operator Splitting for the KdV Equation. Mathematics of Computation, 80, 821-846. https://doi.org/10.1090/S0025-5718-2010-02402-0
|
[17]
|
Holden, H., Lubich, C. and Risebro, N.H. (2012) Operator Splitting for Partial Differential Equations with Burgers Nonlinearity. Mathematics of Computation, 82, 173-185. https://doi.org/10.1090/S0025-5718-2012-02624-X
|
[18]
|
Ma, H. and Sun, W. (2001) Optimal Error Estimates of the Legendre-Petrov-Galerkin Method for the Korteweg-de Vries Equation. SIAM Journal on Numerical Analysis, 39, 1380-1394. https://doi.org/10.1137/S0036142900378327
|
[19]
|
Shen, J. (2003) A New Dual-Petrov-Galerkin Method for Third and Higher Odd-Order Dif- ferential Equations: Application to the KdV Equation. SIAM Journal on Numerical Analysis, 41, 1595-1619. https://doi.org/10.1137/S0036142902410271
|
[20]
|
Yan, J. and Shu, C.W. (2002) A Local Discontinuous Galerkin Method for KdV Type Equa- tions. SIAM Journal on Numerical Analysis, 40, 769-791. https://doi.org/10.1137/S0036142901390378
|
[21]
|
Liu, H. and Yan, J. (2006) A Local Discontinuous Galerkin Method for the Kortewegde Vries Equation with Boundary Effect. Journal of Computational Physics, 215, 197-218. https://doi.org/10.1016/j.jcp.2005.10.016
|
[22]
|
Hochbruck, M. and Ostermann, A. (2010) Exponential Integrators. Acta Numerica, 19, 209-286. https://doi.org/10.1017/S0962492910000048
|
[23]
|
Hofmanov´a, M. and Schratz, K. (2017) An Exponential-Type Integrator for the KdV Equation. Numerische Mathematik, 136, 1117-1137. https://doi.org/10.1007/s00211-016-0859-1
|
[24]
|
Lubich, C. (2008) On Splitting Methods for Schro¨dinger-Poisson and Cubic Nonlinear Schro¨dinger Equations. Mathematics of Computation, 77, 2141-2153. https://doi.org/10.1090/S0025-5718-08-02101-7
|
[25]
|
Ostermann, A. and Schratz, K. (2018) Low Regularity Exponential-Type Integrators for Semi- linear Schr¨odinger Equations. Foundations of Computational Mathematics, 18, 731-755. https://doi.org/10.1007/s10208-017-9352-1
|
[26]
|
Wu, Y. and Yao, F. (2022) A First-Order Fourier Integrator for the Nonlinear Schro¨dinger Equation on T without Loss of Regularity. Mathematics of Computation, 91, 1213-1235. https://doi.org/10.1090/mcom/3705
|
[27]
|
Kato, T. and Ponce, G. (1988) Commutator Estimates and the Euler and Navier-Stokes E- quations. Communications on Pure and Applied Mathematics, 41, 891-907. https://doi.org/10.1002/cpa.3160410704
|