The quadratic B-spline finite-element method for the coupled Schrödinger–Boussinesq equations

References

• Abushama , A. A. and Bialeck , B. 2008 . Modified nodal cubic spline collocation for Possion's equation . SIAM J. Numer. Anal. , 46 : 397 – 418 .
   Web of Science ®Google Scholar
• Bai , D. and Zhang , L. 2009 . The finite element method for the coupled Schrödinger–KdV equations . Phys. Lett. A , 373 : 2237 – 2244 .
   Web of Science ®Google Scholar
• Bogomolov , Y. L. , Kol'chugina , I. A. , Litvak , A. G. and Sergeev , A. M. 1982 . Near-sonic Langmuir solitons . Phys, Lett. A , 91 : 447 – 450 .
   Web of Science ®Google Scholar
• Chen , F. F. 1984 . Introduction to Plasma Physics and Controlled Fusion Plasma Physics , 274 New York : Plenum .
   Google Scholar
• Chowdhury , A. R. , Dasgupta , B. and Rao , N. N. 1998 . Painléve analysis and backlund transformations for coupled generalized Schrödinger–Boussinesq system . Chaos Solitons Fractals , 9 : 1747 – 1753 .
   Web of Science ®Google Scholar
• Ciarlet , P. G. 1978 . The Finite Element Method for Elliptic Problems[M] , Amsterdam : North-Holland .
   Google Scholar
• Fan , E. G. 2003 . An algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolution equations . J. Phys. A: Math. Gen. , 36 : 7009 – 7026 .
   Google Scholar
• Fang , T. K. and Chang , T. N. 2000 . B-spline-based multichannel K-matrix method for atomic photoionization . Phys. Rev. A. , 61 : 062704
   Web of Science ®Google Scholar
• Goldman , M. V. 1984 . Strong turbulence of plasma waves . Rev. Mod. Phys. , 56 : 709 – 735 .
   Web of Science ®Google Scholar
• Guo , B. L. and Du , X. Y. 2001 . Existence of the periodic solution for the weakly damped Schrödinger–Boussinesq equation . J. Math. Anal. Appl. , 262 : 453 – 472 .
   Web of Science ®Google Scholar
• Hase , Y. and Satsuma , J. 1988 . An N-soliton solution for the nonlinear Schrödinger equation coupled to the Boussinesq equation . J. Phys. Soc. Jpn. , 57 : 679 – 682 .
   Google Scholar
• Hasegawa , A. 1975 . Plasma Instabilities and Nonlinear Effects , 194 Berlin : Springer .
   Google Scholar
• Hon , Y. C. and Fan , E. G. 2009 . A series of exact solutions for coupled higgs field equation and coupled Schrödinger–Boussinesq equation . Nonlinear Anal. , 71 : 3501 – 3508 .
   Web of Science ®Google Scholar
• Hu , X. B. , Guo , B. L. and Tam , H. W. 2003 . Homoclinic orbits for the coupled Schrödinger–Boussinesq equation and coupled higgs equation . J. Phys. Soc. Jpn , 72 : 189 – 190 .
   Google Scholar
• Ikezi , H. , Nishikawa , K. and Mima , K. 1974 . Self-modulation of high-frequency electric field and formation of plasma cavities . J. Phys. Soc. Jpn , 37 : 766 – 773 .
   Google Scholar
• Jin , S. , Markowich , P. A. and Zheng , C. 2004 . Numerical simulation of a generalized Zakharov system . J. Comput. Phys. , 201 : 376 – 395 .
   Web of Science ®Google Scholar
• Kingsep , A. S. , Rudakov , L. I. and Sudan , R. N. 1973 . Spectra of strong Langmuir turbulence . Phys. Rev. Lett. , 31 : 1482 – 1484 .
   Web of Science ®Google Scholar
• Liu , C. P. 2005 . Doubly periodic solutions of the coupled scalar field equations . Chaos, Solitons and Fractals , 23 : 93 – 100 .
   Web of Science ®Google Scholar
• Makhankov , V. G. 1974 . On stationary solutions of Schrödinger equation with a self-consistent potential satisfying Boussinesq's equations . Phys. Lett. A , 50 : 42 – 44 .
   Web of Science ®Google Scholar
• Mikkelsen , T. and Pécseli , H. L. 1978 . Investigation of strong turbulence in a low-β plasma . Phys. Rev. Lett. , 41 : 951 – 954 .
   Web of Science ®Google Scholar
• Nishikawa , K. , Hojo , H. , Mima , K. and Ikezi , H. 1974 . Coupled nonlinear electron-plasma and ion-acoustic waves . Phys. Rev. Lett. , 33 : 148 – 151 .
   Web of Science ®Google Scholar
• Panigrahy , M. and Dash , P. C. 1999 . Soliton solutions of a coupled field using the mixing exponential method . Phys. Lett. A , 261 : 284 – 288 .
   Web of Science ®Google Scholar
• Rao , N. N. 1988 . Theory of near-sonic envelope electromagnetic waves in magnetized plasmas . Phys. Rev. A , 37 : 4846 – 4853 .
   Web of Science ®Google Scholar
• Rao , N. N. 1988 . Near-magnetosonic envelope upper-hybrid waves . J. Plasma Phys. , 39 : 385 – 405 .
   Web of Science ®Google Scholar
• Rao , N. N. 1989 . Exact solutions of coupled scalar field equations . J. Phys. A , 22 : 4813 – 4825 .
   Google Scholar
• Rao , N. N. 1996 . Coupled scalar field equations for nonlinear wave modulations in dispersive media . Pramana – J. Phys. , 46 : 161 – 202 .
   Web of Science ®Google Scholar
• Rao , N. N. and Shukla , P. K. 1997 . Coupled Langmuir and ion-acoustic waves in two-electron temperature plasmas . Phys. Plasmas , 4 : 636 – 645 .
   Web of Science ®Google Scholar
• Robinson , P. A. , Newman , D. L. and Goldman , M. V. 1988 . Three-dimensional strong Langmuir turbulence and wave collapse . Phys. Rev. Lett. , 61 : 702 – 705 .
   PubMed Web of Science ®Google Scholar
• Saha , P. , Banerjee , S. and Chowdhury , A. R. 2002 . Normal form analysis and chaotic scenario in a Schrödinger–Boussinesq system . Chaos Solitons Fractals , 14 : 145 – 153 .
   Web of Science ®Google Scholar
• Shatashvili , N. L. and Rao , N. N. 1999 . Localized nonlinear structures of intense electromagnetic waves in two-electron-temperature electron–positron-ion plasmas . Phys. Plasmas , 6 : 66 – 71 .
   Web of Science ®Google Scholar
• Stix , T. H. 1992 . Waves in Plasmas , 294 New York : American Institute of Physics .
   Google Scholar
• Thomee , V. 1984 . Galerkin Finite Element Method for Parabolic Problems , 1054 Berlin : Springer-Verlag . Lecture Notes in Mathematics
   Google Scholar
• Thornhill , S. G. and ter Haar , D. 1978 . Langmuir turbulence and modulational instability . Phys. Rep. , 43 : 43 – 99 .
   Web of Science ®Google Scholar
• Wang , G. and Zhou , Z. 2003 . The Numerical Methods for Differential Equation , China : Higher Education Press .
   Google Scholar
• Wang , X. Y. , Xu , B. C. and Taylor , P. L. 1993 . Exact soliton solutions for a class of coupled field equations . Phys. Lett. A , 173 : 30 – 32 .
   Web of Science ®Google Scholar