메뉴 건너뛰기




Volumn 87, Issue 8, 2010, Pages 1768-1784

Numerical studies on Boussinesq-type equations via a split-step Fourier method

Author keywords

bidirectional solitons; Boussinesq equations; split step Fourier method; water waves

Indexed keywords

BOUSSINESQ EQUATIONS; BOUSSINESQ-TYPE EQUATIONS; DIFFERENTIAL SYSTEMS; FOURIER TRANSFORMATIONS; FOURTH-ORDER RUNGE-KUTTA METHODS; NONLINEAR WAVE EQUATION; SOLI-TARY WAVE SOLUTIONS; SPLIT-STEP FOURIER METHOD;

EID: 77954626424     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/00207160802464597     Document Type: Article
Times cited : (1)

References (22)
  • 1
    • 0037138007 scopus 로고    scopus 로고
    • On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
    • W. Z. Bao, S. Jin, and P. A. Markowich, On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime, J. Comput. Phys. 175(2002), pp. 487-524.
    • (2002) J. Comput. Phys. , vol.175 , pp. 487-524
    • Bao, W.Z.1    Jin, S.2    Markowich, P.A.3
  • 2
    • 0011913755 scopus 로고    scopus 로고
    • Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: Derivation and linear theory
    • J. L. Bona, M. Chen, and J. C. Saut, Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: derivation and linear theory, J. Nonlin. Sci. 12(2002), pp. 283-318.
    • (2002) J. Nonlin. Sci. , vol.12 , pp. 283-318
    • Bona, J.L.1    Chen, M.2    Saut, J.C.3
  • 3
    • 0012698134 scopus 로고    scopus 로고
    • Exact solutions of various Boussinesq systems
    • M. Chen, Exact solutions of various Boussinesq systems, Appl. Math. Lett. 11(1998), pp. 45-49.
    • (1998) Appl. Math. Lett. , vol.11 , pp. 45-49
    • Chen, M.1
  • 4
    • 9544224143 scopus 로고    scopus 로고
    • Multisymplectic geometry, local conservation laws and Fourier pseudospectral discretization for the "good" Boussinesq equation
    • J. B. Chen, Multisymplectic geometry, local conservation laws and Fourier pseudospectral discretization for the "good" Boussinesq equation. Appl. Math. Comput. 161(2005) pp. 55-67.
    • (2005) Appl. Math. Comput. , vol.161 , pp. 55-67
    • Chen, J.B.1
  • 5
    • 0037401905 scopus 로고    scopus 로고
    • Numerical investigation for the solitary waves interaction of the "good" Boussinesq equation
    • H. El-Zoheiry, Numerical investigation for the solitary waves interaction of the "good" Boussinesq equation, Appl. Numer. Math. 45(2003), pp. 161-173.
    • (2003) Appl. Numer. Math. , vol.45 , pp. 161-173
    • El-Zoheiry, H.1
  • 6
    • 0037289935 scopus 로고    scopus 로고
    • A series of traveling wave solutions for two variant Boussinesq equations in shallow water waves
    • E. Fan and Y. C. Hon, A series of traveling wave solutions for two variant Boussinesq equations in shallow water waves, Chaos Soliton Frac. 15(2003), pp. 559-566.
    • (2003) Chaos Soliton Frac , vol.15 , pp. 559-566
    • Fan, E.1    Hon, Y.C.2
  • 7
    • 84966234616 scopus 로고
    • Pseudospectral methods for the "good" Boussinesq equation
    • J. D. E. Frutos, T. Ortega, and J. M. Sanz-Serna, Pseudospectral methods for the "good" Boussinesq equation, Math. Comput. 57(1991), pp. 109-122.
    • (1991) Math. Comput. , vol.57 , pp. 109-122
    • Frutos, J.D.E.1    Ortega, T.2    Sanz-Serna, J.M.3
  • 8
    • 19744363102 scopus 로고    scopus 로고
    • A time-splitting spectral scheme for the Maxwell-Dirac system
    • Z. Huang, S. Jin, P. A. Markowich, and C. Sparber, A time-splitting spectral scheme for the Maxwell-Dirac system, J. Comput. Phys. 208(2005), pp. 761-789.
    • (2005) J. Comput. Phys. , vol.208 , pp. 761-789
    • Huang, Z.1    Jin, S.2    Markowich, P.A.3    Sparber, C.4
  • 9
    • 0037332896 scopus 로고    scopus 로고
    • Bidirectional soliton solutions of the classical Boussinesq system and AKNS system
    • Y. Li and J. E. Zhang, Bidirectional soliton solutions of the classical Boussinesq system and AKNS system, Chaos Soliton Frac. 16(2003), pp. 271-277.
    • (2003) Chaos Soliton Frac , vol.16 , pp. 271-277
    • Li, Y.1    Zhang, J.E.2
  • 11
    • 0037284595 scopus 로고    scopus 로고
    • A split-step Fourier method for the complex modified Korteweg-de Vries equation
    • G. M. Muslu and H. A. Erbay, A split-step Fourier method for the complex modified Korteweg-de Vries equation. Comput. Math. Appl. 45(2003), pp. 503-514.
    • (2003) Comput. Math. Appl. , vol.45 , pp. 503-514
    • Muslu, G.M.1    Erbay, H.A.2
  • 12
    • 10644227675 scopus 로고    scopus 로고
    • Higher-order split-step Fourier schemes for the generalized Schrödinger equation
    • G. M. Muslu and H. A. Erbay, Higher-order split-step Fourier schemes for the generalized Schrödinger equation, Math. Comput. Simul. 67(2005), pp. 581-595.
    • (2005) Math. Comput. Simul , vol.67 , pp. 581-595
    • Muslu, G.M.1    Erbay, H.A.2
  • 13
    • 0000511098 scopus 로고
    • Nonlinear stability and convergence of finite-difference methods for the "good" Boussinesq equation
    • T. Ortega and J. M. Sanz-Serna, Nonlinear stability and convergence of finite-difference methods for the "good" Boussinesq equation. Numer. Math. 58(1990), pp. 215-229.
    • (1990) Numer. Math. , vol.58 , pp. 215-229
    • Ortega, T.1    Sanz-Serna, J.M.2
  • 14
    • 0034911329 scopus 로고    scopus 로고
    • Numerical modeling of two-way propagation of nonlinear dispersive waves
    • B. Pelloni and V. A. Dougalis, Numerical modeling of two-way propagation of nonlinear dispersive waves, Math. Comput. Simul. 55(2001), pp. 595-606.
    • (2001) Math. Comput. Simul , vol.55 , pp. 595-606
    • Pelloni, B.1    Dougalis, V.A.2
  • 15
    • 84888282424 scopus 로고    scopus 로고
    • Numerical methods for bi-directional soliton problems
    • H. Rong and R. X. Liu, Numerical methods for bi-directional soliton problems, J. Univ. Sci. Tech. China 34(2004), pp. 295-306.
    • (2004) J. Univ. Sci. Tech. China , vol.34 , pp. 295-306
    • Rong, H.1    Liu, R.X.2
  • 16
    • 0031922993 scopus 로고    scopus 로고
    • Spectral modeling of nonlinear dispersive waves
    • B. F. Sanders, N. D. Katopodes, and J. P. Boyd, Spectral modeling of nonlinear dispersive waves, J. Hydraulic Eng. 124(1998), pp. 2-12.
    • (1998) J. Hydraulic Eng. , vol.124 , pp. 2-12
    • Sanders, B.F.1    Katopodes, N.D.2    Boyd, J.P.3
  • 17
    • 0001518684 scopus 로고
    • On the construction and comparison of difference scheme
    • G. Strang, On the construction and comparison of difference scheme, SIAM J. Numer. Anal. 5(1968), pp. 506-517.
    • (1968) SIAM J. Numer. Anal. , vol.5 , pp. 506-517
    • Strang, G.1
  • 18
    • 0000251609 scopus 로고
    • Numerical solutions of the Korteweg-de Vries equation and its generalizations by the split-step Fourier method
    • A. C. Newell ed., Lect. Appl. Math., Amer. Math. Soc., Providence, RI
    • F. Tappert, Numerical solutions of the Korteweg-de Vries equation and its generalizations by the split-step Fourier method, in Nonlinear Wave Motion, A. C. Newell ed., Lect. Appl. Math., Amer. Math. Soc., Providence, RI 15(1974), pp. 215-216.
    • (1974) Nonlinear Wave Motion , vol.15 , pp. 215-216
    • Tappert, F.1
  • 20
    • 0002158048 scopus 로고    scopus 로고
    • On modeling nonlinear long waves
    • L. P. Cook, V. Royturb, and M. Tubin, eds., SIAM, Philadelphia
    • T. Y. Wu and J. E. Zhang, On modeling nonlinear long waves, in Mathematics is for Solving Problems, L. P. Cook, V. Royturb, and M. Tubin, eds., SIAM, Philadelphia, 1996, pp. 233-241.
    • (1996) Mathematics is for Solving Problems , pp. 233-241
    • Wu, T.Y.1    Zhang, J.E.2
  • 21
    • 0037718267 scopus 로고    scopus 로고
    • Bidirectional solitons on water
    • J. E. Zhang and Y. Li, Bidirectional solitons on water, Phys. Rev. E 67(2003), pp. 016306.
    • (2003) Phys. Rev. E , vol.67 , pp. 016306
    • Zhang, J.E.1    Li, Y.2
  • 22
    • 2442712497 scopus 로고    scopus 로고
    • On Boussinesq models of constant depth
    • J. E. Zhang, C. Chen, and Y. Li, On Boussinesq models of constant depth, Phys. Fluids 16(2004), pp. 1287-1296.
    • (2004) Phys. Fluids , vol.16 , pp. 1287-1296
    • Zhang, J.E.1    Chen, C.2    Li, Y.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.