References
- D.M. Bai and J.L. Wang, The time-splitting Fourier spectral method for the coupled Schrödinger -Boussinesq equations, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), pp. 1201–1210. doi: 10.1016/j.cnsns.2011.08.012
- D.M. Bai and L.M. Zhang, The quadratic B-spline finite element method for the coupled Schrödinger-Boussinesq equations, Inter. J. Comput. Math. 88 (2011), pp. 1714–1729. doi: 10.1080/00207160.2010.522234
- C. Banquet, L.C. Ferreira, and E.J. Villamizar-Roa, On the Schrödinger-Boussinesq system with singular initial data, J. Math. Anal. Appl. 400 (2013), pp. 487–496. doi: 10.1016/j.jmaa.2012.10.047
- W.Z. Bao and Y.Y. Cai, Uniform and optimal error estimates of an exponential wave integrator sine pseudospectral method for the nonlinear Schrödinger equation with wave operator, SIAM J. Numer. Anal. 52 (2014), pp. 1103–1127. doi: 10.1137/120866890
- W.Z. Bao, Y.Y. Cai, X.W. Jia, and J. Yin, Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime, Sci. Chin. Math. 59 (2016), pp. 1461–1494. doi: 10.1007/s11425-016-0272-y
- W.Z. Bao and X.C. Dong, Analysis and comparison of numerical methods for the Klein-Gordon equation in the nonrelativistic limit regime, Numer. Math. 120 (2012), pp. 189–229. doi: 10.1007/s00211-011-0411-2
- W.Z. Bao, X.C. Dong, and X.F. Zhao, An exponential wave integrator sine pseudospectral method for the Klein Gordon Zakharov system, SIAM J. Sci. Comput. 35 (2013), pp. A2903–A2927. doi: 10.1137/110855004
- X.C. Dong, A trigonometric integrator pseudospectral discretization for the N-coupled nonlinear Klein-Gordon equations, Numer. Algor. 62 (2013), pp. 325–336. doi: 10.1007/s11075-012-9586-6
- X.C. Dong, Stability and convergence of trigonometric integrator pseudospectral discretization for N-coupled nonlinear Klein-Gordon equations, Appl. Math. Comput. 232 (2014), pp. 752–765.
- L.G. Farah and A. Pastor, On the periodic Schrödinger-Boussinesq system, J. Math. Anal. Appl.368 (2010), pp. 330–349. doi: 10.1016/j.jmaa.2010.03.007
- W. Gautschi, Numerical integration of ordinary differential equations based on trigonometric polynomials, Numer. Math. 3 (1961), pp. 381–397. doi: 10.1007/BF01386037
- V. Grimm, A note on the Gautschi-type method for oscillatory second-order differential equations, Numer. Math. 102 (2005), pp. 61–66. doi: 10.1007/s00211-005-0639-9
- V. Grimm, On error bounds for the Gautschi-type exponential wave integrator applied to oscillatory second order differential equations, Numer. Math. 100 (2005), pp. 71–89. doi: 10.1007/s00211-005-0583-8
- M.J. Guan and Y.S. Li, Periodic solution of weakly damped 3D Schrödinger-Boussinesq equations, Chin. Quart. J. Math. 18 (2003), pp. 31–337.
- B.L. Guo and F.X. Chen, Finite dimensional behavior of global attractors for weakly damped nonlinear Schrödinger-Boussinesq equations, Phys. D. 93 (1996), pp. 101–118. doi: 10.1016/0167-2789(95)00277-4
- L.J. Han, J.J. Zhang, and B.L. Guo, Global well-posedness for the fractional Schrödinger-Boussinesq system, Commun. Nonlinear Sci. Numer. Simul. 19 (2014), pp. 2644–2652. doi: 10.1016/j.cnsns.2013.12.032
- Y.S. Li and Q.Y. Chen, Finite dimensional global attractor for dissipative Schrödinger-Boussinesq equations, J. Math. Anal. Appl. 205 (1997), pp. 107–132. doi: 10.1006/jmaa.1996.5148
- F. Liao and L.M. Zhang, Conservative compact finite difference scheme for the coupled Schrö dinger-Boussinesq equation, Numer. Methods Part Differ. Equ. 32 (2016), pp. 1667–1688. doi: 10.1002/num.22067
- F. Liao, L.M. Zhang, and S.S. Wang, Numerical analysis of cubic spline collocation methods for the coupled Schrödinger-Boussinesq equations, Appl. Numer. Math. 119 (2017), pp. 194–212. doi: 10.1016/j.apnum.2017.04.007
- F. Liao, L.M. Zhang, and S.S. Wang, Time-splitting combined with exponential wave integrator Fourier pseudospectral method for Schrödinger-Boussinesq equations, Commun. Nonlinear Sci. Numer. Simul. 55 (2018), pp. 93–104. doi: 10.1016/j.cnsns.2017.06.033
- N.N. Rao, Coupled scalar field equations for nonlinear wave modulations in dispersive media, Pramana J. Pyhs. 46 (1991), pp. 161–202. doi: 10.1007/BF02846945
- J. Shen, T. Tang, and L.L. Wang, Spectral Methods: Algorithms, Analysis and Applications, Springer Verilag, Berlin Heidelberg, 2011.
- B.N. Sun and Z. Lian, Rogue waves in the multicomponent Mel'nikov system and multicomponent Schrödinger-Boussinesq system, Pramana J. Phys. 90 (2018), pp. 1–23. doi: 10.1007/s12043-017-1512-y
- Z.G. Xu, X.C. Dong, and Y.J. Yuan, Error estimates in the energy space for a Gautschi-type integrator spectral discretization for the coupled nonlinear Klein-Gordon equations, J. Comput. Appl. Math. 292 (2016), pp. 402–416. doi: 10.1016/j.cam.2015.07.017
- L.M. Zhang, D.M. Bai, and S.S. Wang, Numerical analysis for a conservative difference scheme to solve the Schrödinger-Boussinesq equation, J. Comput. Appl. Math. 235 (2011), pp. 4899–4915. doi: 10.1016/j.cam.2011.04.001
- X.F. Zhao, An exponential wave integrator pseudospectral method for the symmetric regularized long wave equation, J. Comput. Math. 34 (2016), pp. 49–69. doi: 10.4208/jcm.1510-m4467
- X.F. Zhao, On error estimates of an exponential wave integrator sine pseudospectral method for the Klein Gordon Zakharov system, Numer. Methods Part Differ. Equ. 32 (2016), pp. 266–291. doi: 10.1002/num.21994
- J.D. Zheng and X.M. Xiang, The finite element analysis for the equation system coupling the complex Schrödinger and real Boussinesq fields, Math. Numer. Sinica 5 (1987), pp. 133–143. ( in Chinese).