메뉴 건너뛰기




Volumn 17, Issue 12, 2012, Pages 4602-4610

Numerical solution of nonlinear Jaulent-Miodek and Whitham-Broer-Kaup equations

Author keywords

Exponential time differencing; High accuracy; Integrating factor; Jaulent Miodek equation; Spectral methods; Whitham Broer Kaup equation

Indexed keywords

MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS;

EID: 84864405118     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2012.04.011     Document Type: Article
Times cited : (20)

References (35)
  • 3
    • 0036501083 scopus 로고    scopus 로고
    • Exponential time differencing for stiff systems
    • Cox S.M., Matthews P.C. Exponential time differencing for stiff systems. J Comput Phys 2002, 176:430-455.
    • (2002) J Comput Phys , vol.176 , pp. 430-455
    • Cox, S.M.1    Matthews, P.C.2
  • 4
    • 0001332722 scopus 로고    scopus 로고
    • Explosion of soliton in a multicomponent plasma
    • Das G.C. Explosion of soliton in a multicomponent plasma. Phys Plasmas 1997, 4:2095-2100.
    • (1997) Phys Plasmas , vol.4 , pp. 2095-2100
    • Das, G.C.1
  • 5
    • 80052323256 scopus 로고    scopus 로고
    • The solitary wave solution of the two-dimensional regularized long-wave equation in fluids and plasmas
    • Dehghan M., Salehi R. The solitary wave solution of the two-dimensional regularized long-wave equation in fluids and plasmas. Comput Phys Commun 2011, 182:2540-2549.
    • (2011) Comput Phys Commun , vol.182 , pp. 2540-2549
    • Dehghan, M.1    Salehi, R.2
  • 6
    • 61549088742 scopus 로고    scopus 로고
    • Meshless local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity
    • Dehghan M., Mirzaei D. Meshless local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity. Appl Numer Math 2009, 59:1043-1058.
    • (2009) Appl Numer Math , vol.59 , pp. 1043-1058
    • Dehghan, M.1    Mirzaei, D.2
  • 7
    • 77954800929 scopus 로고    scopus 로고
    • Application of semi-analytic methods for the Fitzhugh-Nagumo equation which models the transmission of nerve impulses
    • Dehghan M., Manafian Heris J., Saadatmandi A. Application of semi-analytic methods for the Fitzhugh-Nagumo equation which models the transmission of nerve impulses. Math Methods Appl Sci 2010, 33:1384-1398.
    • (2010) Math Methods Appl Sci , vol.33 , pp. 1384-1398
    • Dehghan, M.1    Manafian Heris, J.2    Saadatmandi, A.3
  • 8
    • 56149124076 scopus 로고    scopus 로고
    • A numerical method for solution of the two-dimensional Sine-Gordon equation using the radial basis functions
    • Dehghan M., Shokri A. A numerical method for solution of the two-dimensional Sine-Gordon equation using the radial basis functions. Math Comput Simul 2008, 79:700-715.
    • (2008) Math Comput Simul , vol.79 , pp. 700-715
    • Dehghan, M.1    Shokri, A.2
  • 9
    • 27144518174 scopus 로고    scopus 로고
    • Analysis and applications of the exponential time differencing schemes and their contour integration modifications
    • Du Q., Zhu W. Analysis and applications of the exponential time differencing schemes and their contour integration modifications. BIT Numer Math 2005, 45:307-328.
    • (2005) BIT Numer Math , vol.45 , pp. 307-328
    • Du, Q.1    Zhu, W.2
  • 10
    • 25144432847 scopus 로고    scopus 로고
    • Exact and numerical traveling wave solutions of Whitham-Broer-Kaup equations
    • El-Sayed S.M., Kaya D. Exact and numerical traveling wave solutions of Whitham-Broer-Kaup equations. Appl Math Comput 2005, 167:1339-1349.
    • (2005) Appl Math Comput , vol.167 , pp. 1339-1349
    • El-Sayed, S.M.1    Kaya, D.2
  • 11
    • 0037408898 scopus 로고    scopus 로고
    • Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics
    • Fan E. Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics. Chaos Solitons Fract 2003, 16:819-839.
    • (2003) Chaos Solitons Fract , vol.16 , pp. 819-839
    • Fan, E.1
  • 12
    • 0001444952 scopus 로고    scopus 로고
    • A fast spectral algorithm for nonlinear wave equations with linear dispersion
    • Fornberg B., Driscoll T.A. A fast spectral algorithm for nonlinear wave equations with linear dispersion. J Comput Phys 1999, 155:456-467.
    • (1999) J Comput Phys , vol.155 , pp. 456-467
    • Fornberg, B.1    Driscoll, T.A.2
  • 13
    • 77955468074 scopus 로고    scopus 로고
    • Approximate traveling wave solutions for coupled Whitham-Broer-Kaup shallow water
    • Ganji D.D., Rokni H.B., Sfahani M.G., Ganji S.S. Approximate traveling wave solutions for coupled Whitham-Broer-Kaup shallow water. Adv Eng Soft 2010, 41:956-961.
    • (2010) Adv Eng Soft , vol.41 , pp. 956-961
    • Ganji, D.D.1    Rokni, H.B.2    Sfahani, M.G.3    Ganji, S.S.4
  • 14
    • 34250650099 scopus 로고    scopus 로고
    • Application of He's variational iteration method to nonlinear Jaulent-Miodek equations and comparing it with ADM
    • Ganji D.D., Jannatabadi M., Mohseni E. Application of He's variational iteration method to nonlinear Jaulent-Miodek equations and comparing it with ADM. J Comput Appl Math 2007, 207:35-45.
    • (2007) J Comput Appl Math , vol.207 , pp. 35-45
    • Ganji, D.D.1    Jannatabadi, M.2    Mohseni, E.3
  • 15
    • 38649132547 scopus 로고    scopus 로고
    • Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method
    • He J-H., Zhang L-N. Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method. Phys Lett A 2008, 372(7):1044-1047.
    • (2008) Phys Lett A , vol.372 , Issue.7 , pp. 1044-1047
    • He, J.-H.1    Zhang, L.-N.2
  • 16
    • 0032355046 scopus 로고    scopus 로고
    • Bogoliubov quasiparticles carried by dark solitonic excitations in nonuniform Bose-Einstein condensates
    • Hong T., Wang Y.Z., Huo Y.S. Bogoliubov quasiparticles carried by dark solitonic excitations in nonuniform Bose-Einstein condensates. Chin Phys Lett 1998, 15:550-552.
    • (1998) Chin Phys Lett , vol.15 , pp. 550-552
    • Hong, T.1    Wang, Y.Z.2    Huo, Y.S.3
  • 17
    • 22544474620 scopus 로고    scopus 로고
    • Fourth-order time-stepping for stiff PDEs
    • Kassam A.K., Trefethen L.N. Fourth-order time-stepping for stiff PDEs. SIAM J Sci Comput 2005, 26:1214-1233.
    • (2005) SIAM J Sci Comput , vol.26 , pp. 1214-1233
    • Kassam, A.K.1    Trefethen, L.N.2
  • 18
    • 0242428849 scopus 로고    scopus 로고
    • A numerical method for solving Jaulent-Miodek equation
    • Kaya D., El-Sayed S.M. A numerical method for solving Jaulent-Miodek equation. Phys Lett A 2003, 318:345-353.
    • (2003) Phys Lett A , vol.318 , pp. 345-353
    • Kaya, D.1    El-Sayed, S.M.2
  • 19
    • 66149158575 scopus 로고    scopus 로고
    • Cusp-like singular soliton solutions of Jaulent-Miodek equation using symbolic computation
    • Kavitha L., Satishkumar P., Nathiyaa T., Gopi D. Cusp-like singular soliton solutions of Jaulent-Miodek equation using symbolic computation. Phys Scripta 2009, 79:035403.
    • (2009) Phys Scripta , vol.79 , pp. 035403
    • Kavitha, L.1    Satishkumar, P.2    Nathiyaa, T.3    Gopi, D.4
  • 20
    • 61849130653 scopus 로고    scopus 로고
    • Application of meshfree collocation method to a class of nonlinear partial differential equations
    • Khatack A.J., Tirmizi S.I.A., Siraj-ul-Islam Application of meshfree collocation method to a class of nonlinear partial differential equations. Eng Anal Bound Elem 2009, 33:661-667.
    • (2009) Eng Anal Bound Elem , vol.33 , pp. 661-667
    • Khatack, A.J.1    Tirmizi, S.I.A.2    Siraj-ul-Islam3
  • 21
    • 10844237437 scopus 로고    scopus 로고
    • Generalized integrating factor methods for stiff PDEs
    • Krogstad S. Generalized integrating factor methods for stiff PDEs. J Comput Phys 2005, 203:72-88.
    • (2005) J Comput Phys , vol.203 , pp. 72-88
    • Krogstad, S.1
  • 22
    • 34250112720 scopus 로고
    • Mathematics of dispersive water waves
    • Kupershmidt B.A. Mathematics of dispersive water waves. Commun Math Phys 1985, 99:51-73.
    • (1985) Commun Math Phys , vol.99 , pp. 51-73
    • Kupershmidt, B.A.1
  • 23
    • 0033469511 scopus 로고    scopus 로고
    • A direct perturbation method: nonlinear Schrodinger equation with loss
    • Lou S.Y. A direct perturbation method: nonlinear Schrodinger equation with loss. Chin Phys Lett 1999, 16:659-661.
    • (1999) Chin Phys Lett , vol.16 , pp. 659-661
    • Lou, S.Y.1
  • 24
    • 63449113626 scopus 로고    scopus 로고
    • A second Wronskian formulation of the Boussinesq equation
    • Ma W.X., Li C.X., He J.S. A second Wronskian formulation of the Boussinesq equation. Nonlinear Anal 2009, 70:4245-4258.
    • (2009) Nonlinear Anal , vol.70 , pp. 4245-4258
    • Ma, W.X.1    Li, C.X.2    He, J.S.3
  • 25
    • 84862777329 scopus 로고    scopus 로고
    • Hirota bilinear equations with linear subspaces of solutions
    • Ma W.X., Zhang Y., Tang Y., Tu J. Hirota bilinear equations with linear subspaces of solutions. Appl Math Comput 2012, 218:174-7183.
    • (2012) Appl Math Comput , vol.218 , pp. 174-7183
    • Ma, W.X.1    Zhang, Y.2    Tang, Y.3    Tu, J.4
  • 26
    • 80052336619 scopus 로고    scopus 로고
    • Efficient numerical algorithms for the solution of "good" Boussinesq equation in water wave propagation
    • Mohebbi A., Asgari Z. Efficient numerical algorithms for the solution of "good" Boussinesq equation in water wave propagation. Comput Phys Commun 2011, 182:2464-2470.
    • (2011) Comput Phys Commun , vol.182 , pp. 2464-2470
    • Mohebbi, A.1    Asgari, Z.2
  • 27
    • 77957893666 scopus 로고    scopus 로고
    • A Not-a-Knot meshless method using radial basis functions and predictor-corrector scheme to the numerical solution of improved Boussinesq equation
    • Shokri A., Dehghan M. A Not-a-Knot meshless method using radial basis functions and predictor-corrector scheme to the numerical solution of improved Boussinesq equation. Comput Phys Commun 2010, 181:1990-2000.
    • (2010) Comput Phys Commun , vol.181 , pp. 1990-2000
    • Shokri, A.1    Dehghan, M.2
  • 28
    • 34250696383 scopus 로고    scopus 로고
    • On the convergence of He's variational iteration method
    • Tatari M., Dehghan M. On the convergence of He's variational iteration method. J Comput Appl Math 2007, 207:121-128.
    • (2007) J Comput Appl Math , vol.207 , pp. 121-128
    • Tatari, M.1    Dehghan, M.2
  • 29
    • 33947173172 scopus 로고    scopus 로고
    • Nonlinear Schrodinger equations and N=1 superconformal algebra
    • Ozer H.T., Salihoglu S. Nonlinear Schrodinger equations and N=1 superconformal algebra. Chaos Solitons Fract 2007, 33:1417-1423.
    • (2007) Chaos Solitons Fract , vol.33 , pp. 1417-1423
    • Ozer, H.T.1    Salihoglu, S.2
  • 31
    • 34247562366 scopus 로고    scopus 로고
    • The tanh-coth and the sech methods for exact solutions of the Jaulent-Miodek equation
    • Wazwaz A.M. The tanh-coth and the sech methods for exact solutions of the Jaulent-Miodek equation. Phys Lett A 2007, 366:85-90.
    • (2007) Phys Lett A , vol.366 , pp. 85-90
    • Wazwaz, A.M.1
  • 32
    • 0035948195 scopus 로고    scopus 로고
    • Explicit and exact traveling wave solutions of Whitham-Broer-Kaup shallow water equations
    • Xie F., Yan Z., Zhang H. Explicit and exact traveling wave solutions of Whitham-Broer-Kaup shallow water equations. Phys Lett A 2001, 28:76-80.
    • (2001) Phys Lett A , vol.28 , pp. 76-80
    • Xie, F.1    Yan, Z.2    Zhang, H.3
  • 33
    • 10844263247 scopus 로고    scopus 로고
    • Exact traveling wave solutions of the Whitham-Broer-Kaup and Broer-Kaup-Kupershmidt equations
    • Xu G., Li Z. Exact traveling wave solutions of the Whitham-Broer-Kaup and Broer-Kaup-Kupershmidt equations. Chaos Solitons Fract 2005, 24:549-556.
    • (2005) Chaos Solitons Fract , vol.24 , pp. 549-556
    • Xu, G.1    Li, Z.2
  • 34
    • 0033432463 scopus 로고    scopus 로고
    • Multiple soliton solutions of the dispersive long-wave equations
    • Zhang J.F. Multiple soliton solutions of the dispersive long-wave equations. Chin Phys Lett 1999, 16:4-6.
    • (1999) Chin Phys Lett , vol.16 , pp. 4-6
    • Zhang, J.F.1
  • 35
    • 70349985711 scopus 로고    scopus 로고
    • Application of Exp-function method to the Whitham-Broer-Kaup shallow water model using symbolic computation
    • Zheng Z., Shan W.R. Application of Exp-function method to the Whitham-Broer-Kaup shallow water model using symbolic computation. Appl Math Comput 2009, 215:2390-2396.
    • (2009) Appl Math Comput , vol.215 , pp. 2390-2396
    • Zheng, Z.1    Shan, W.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.