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Volumn 204, Issue 2, 2008, Pages 942-948

Multiple soliton solutions and multiple singular soliton solutions for the (3 + 1)-dimensional Burgers equations

Author keywords

(3 + 1) Dimensional Burgers equations; Hirota bilinear method; Kink solutions; Singular kink solutions; Tanh coth method

Indexed keywords

BARIUM; TURBULENCE;

EID: 53449088720     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.08.004     Document Type: Article
Times cited : (30)

References (30)
  • 1
    • 1042302422 scopus 로고    scopus 로고
    • Symmetries and strong symmetries of the (3 + 1)-dimensional Burgers equation
    • Ju L.Z., and Yue L.S. Symmetries and strong symmetries of the (3 + 1)-dimensional Burgers equation. Chin. Phys. Lett. 21 (2004) 219-222
    • (2004) Chin. Phys. Lett. , vol.21 , pp. 219-222
    • Ju, L.Z.1    Yue, L.S.2
  • 2
    • 0141567689 scopus 로고    scopus 로고
    • Multilinear variable separation approach in (3 + 1)-dimensions: the Burgers equation
    • Ping Y.J., and Yue L.S. Multilinear variable separation approach in (3 + 1)-dimensions: the Burgers equation. Chin. Phys. Lett. 20 (2003) 1448-1451
    • (2003) Chin. Phys. Lett. , vol.20 , pp. 1448-1451
    • Ping, Y.J.1    Yue, L.S.2
  • 3
    • 3242759876 scopus 로고    scopus 로고
    • New exact solution to (3 + 1)-dimensional Burgers equation
    • Peng S.S., Liang P.Z., and Jun Z. New exact solution to (3 + 1)-dimensional Burgers equation. Commun. Theor. Phys. 42 (2004) 49-50
    • (2004) Commun. Theor. Phys. , vol.42 , pp. 49-50
    • Peng, S.S.1    Liang, P.Z.2    Jun, Z.3
  • 4
    • 43049116456 scopus 로고    scopus 로고
    • Symbolic computation and non-travelling wave solutions of (2 + 1)-dimensional nonlinear evolution equations
    • Wang D.-S., and Li H. Symbolic computation and non-travelling wave solutions of (2 + 1)-dimensional nonlinear evolution equations. Chaos Solitons Fract. 38 (2008) 383-390
    • (2008) Chaos Solitons Fract. , vol.38 , pp. 383-390
    • Wang, D.-S.1    Li, H.2
  • 5
    • 18444379366 scopus 로고    scopus 로고
    • A new Riccati equation rational expansion method and its application to (2 + 1)-dimensional Burgers equation
    • Wang Q., Chen Y., and Zhang H. A new Riccati equation rational expansion method and its application to (2 + 1)-dimensional Burgers equation. Chaos Solitons Fract. 25 (2005) 1019-1028
    • (2005) Chaos Solitons Fract. , vol.25 , pp. 1019-1028
    • Wang, Q.1    Chen, Y.2    Zhang, H.3
  • 6
    • 0037351075 scopus 로고    scopus 로고
    • Variable separation solutions for the (2 + 1)-dimensional Burgers equation
    • Tang X.Y., and Lou S. Variable separation solutions for the (2 + 1)-dimensional Burgers equation. Chin. Phys. Lett. 20 (2003) 335-337
    • (2003) Chin. Phys. Lett. , vol.20 , pp. 335-337
    • Tang, X.Y.1    Lou, S.2
  • 7
    • 0000293426 scopus 로고
    • Resonance of solitons in one dimension
    • Hirota R., and Ito M. Resonance of solitons in one dimension. J. Phys. Soc. Jpn. 52 3 (1983) 744-748
    • (1983) J. Phys. Soc. Jpn. , vol.52 , Issue.3 , pp. 744-748
    • Hirota, R.1    Ito, M.2
  • 8
    • 0000531288 scopus 로고
    • An extension of nonlinear evolution equations of the K-dV (mK-dV) type to higher order
    • Ito M. An extension of nonlinear evolution equations of the K-dV (mK-dV) type to higher order. J. Phys. Soc. Jpn. 49 2 (1980) 771-778
    • (1980) J. Phys. Soc. Jpn. , vol.49 , Issue.2 , pp. 771-778
    • Ito, M.1
  • 9
    • 56249128025 scopus 로고
    • N-Soliton solutions of model equations for shallow water waves
    • Hirota R., and Satsuma J. N-Soliton solutions of model equations for shallow water waves. J. Phys. Soc. Jpn. 40 2 (1976) 611-612
    • (1976) J. Phys. Soc. Jpn. , vol.40 , Issue.2 , pp. 611-612
    • Hirota, R.1    Satsuma, J.2
  • 10
    • 0001247353 scopus 로고
    • A new form of Bäcklund transformations and its relation to the inverse scattering problem
    • Hirota R. A new form of Bäcklund transformations and its relation to the inverse scattering problem. Prog. Theor. Phys. 52 5 (1974) 1498-1512
    • (1974) Prog. Theor. Phys. , vol.52 , Issue.5 , pp. 1498-1512
    • Hirota, R.1
  • 12
    • 35949040541 scopus 로고
    • Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons
    • Hirota R. Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27 18 (1971) 1192-1194
    • (1971) Phys. Rev. Lett. , vol.27 , Issue.18 , pp. 1192-1194
    • Hirota, R.1
  • 13
    • 0001486467 scopus 로고
    • A search for bilinear equations passing Hirota's three-soliton condition. I. KdV-type bilinear equations
    • Hietarinta J. A search for bilinear equations passing Hirota's three-soliton condition. I. KdV-type bilinear equations. J. Math. Phys. 28 8 (1987) 1732-1742
    • (1987) J. Math. Phys. , vol.28 , Issue.8 , pp. 1732-1742
    • Hietarinta, J.1
  • 14
    • 0039623545 scopus 로고
    • A search for bilinear equations passing Hirota's three-soliton condition. II. mKdV-type bilinear equations
    • Hietarinta J. A search for bilinear equations passing Hirota's three-soliton condition. II. mKdV-type bilinear equations. J. Math. Phys. 28 9 (1987) 2094-2101
    • (1987) J. Math. Phys. , vol.28 , Issue.9 , pp. 2094-2101
    • Hietarinta, J.1
  • 15
    • 53449095848 scopus 로고    scopus 로고
    • W. Hereman, W. Zhuang, A MACSYMA program for the Hirota method, in: Proceedings of the 13th World Congress on Computation and Applied Mathematics, vol. 2, 1991, pp. 842-863.
    • W. Hereman, W. Zhuang, A MACSYMA program for the Hirota method, in: Proceedings of the 13th World Congress on Computation and Applied Mathematics, vol. 2, 1991, pp. 842-863.
  • 17
    • 53449085568 scopus 로고    scopus 로고
    • W. Hereman, W. Zhuang, A MACSYMA program for the Hirota method, in: Proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics, 1991, pp. 22-26.
    • W. Hereman, W. Zhuang, A MACSYMA program for the Hirota method, in: Proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics, 1991, pp. 22-26.
  • 18
    • 1442264988 scopus 로고    scopus 로고
    • The tanh method: a tool for solving certain classes of nonlinear evolution and wave equations
    • Malfliet W. The tanh method: a tool for solving certain classes of nonlinear evolution and wave equations. J. Comput. Appl. Math. 164-165 (2004) 529-541
    • (2004) J. Comput. Appl. Math. , vol.164-165 , pp. 529-541
    • Malfliet, W.1
  • 19
    • 0001229736 scopus 로고
    • Solitary wave solutions of nonlinear wave equations
    • Malfliet W. Solitary wave solutions of nonlinear wave equations. Am. J. Phys. 60 7 (1992) 650-654
    • (1992) Am. J. Phys. , vol.60 , Issue.7 , pp. 650-654
    • Malfliet, W.1
  • 20
    • 0004483962 scopus 로고    scopus 로고
    • The tanh method. I: Exact solutions of nonlinear evolution and wave equations
    • Malfliet W., and Hereman W. The tanh method. I: Exact solutions of nonlinear evolution and wave equations. Phys. Scripta 54 (1996) 563-568
    • (1996) Phys. Scripta , vol.54 , pp. 563-568
    • Malfliet, W.1    Hereman, W.2
  • 21
    • 0000068096 scopus 로고    scopus 로고
    • The tanh method. II: Perturbation technique for conservative systems
    • Malfliet W., and Hereman W. The tanh method. II: Perturbation technique for conservative systems. Phys. Scripta 54 (1996) 569-575
    • (1996) Phys. Scripta , vol.54 , pp. 569-575
    • Malfliet, W.1    Hereman, W.2
  • 22
    • 34249786250 scopus 로고    scopus 로고
    • Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method
    • Wazwaz A.M. Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method. Appl. Math. Comput. 190 (2007) 633-640
    • (2007) Appl. Math. Comput. , vol.190 , pp. 633-640
    • Wazwaz, A.M.1
  • 23
    • 34250643151 scopus 로고    scopus 로고
    • Multiple-front solutions for the Burgers equation and the coupled Burgers equations
    • Wazwaz A.M. Multiple-front solutions for the Burgers equation and the coupled Burgers equations. Appl. Math. Comput. 190 (2007) 1198-1206
    • (2007) Appl. Math. Comput. , vol.190 , pp. 1198-1206
    • Wazwaz, A.M.1
  • 24
    • 34249735366 scopus 로고    scopus 로고
    • New solitons and kink solutions for the Gardner equation
    • Wazwaz A.M. New solitons and kink solutions for the Gardner equation. Commun. Nonlinear Sci. Numer. Simul. 12 8 (2007) 1395-1404
    • (2007) Commun. Nonlinear Sci. Numer. Simul. , vol.12 , Issue.8 , pp. 1395-1404
    • Wazwaz, A.M.1
  • 25
    • 34548823237 scopus 로고    scopus 로고
    • Multiple-soliton solutions for the Boussinesq equation
    • Wazwaz A.M. Multiple-soliton solutions for the Boussinesq equation. Appl. Math. Comput. 192 (2007) 479-486
    • (2007) Appl. Math. Comput. , vol.192 , pp. 479-486
    • Wazwaz, A.M.1
  • 26
    • 41949134292 scopus 로고    scopus 로고
    • The Hirota's direct method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Ito seventh-order equation
    • Wazwaz A.M. The Hirota's direct method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Ito seventh-order equation. Appl. Math. Comput. 199 1 (2008) 133-138
    • (2008) Appl. Math. Comput. , vol.199 , Issue.1 , pp. 133-138
    • Wazwaz, A.M.1
  • 27
    • 43049165451 scopus 로고    scopus 로고
    • Multiple-front solutions for the Burgers-Kadomtsev-Petvisahvili equation
    • Wazwaz A.M. Multiple-front solutions for the Burgers-Kadomtsev-Petvisahvili equation. Appl. Math. Comput. 200 (2008) 437-443
    • (2008) Appl. Math. Comput. , vol.200 , pp. 437-443
    • Wazwaz, A.M.1
  • 28
    • 44649142146 scopus 로고    scopus 로고
    • Multiple-soliton solutions for the Lax-Kadomtsev-Petvisahvili (Lax-KP) equation
    • Wazwaz A.M. Multiple-soliton solutions for the Lax-Kadomtsev-Petvisahvili (Lax-KP) equation. Appl. Math. Comput. 201 1/2 (2008) 168-174
    • (2008) Appl. Math. Comput. , vol.201 , Issue.1-2 , pp. 168-174
    • Wazwaz, A.M.1
  • 29
    • 44649165713 scopus 로고    scopus 로고
    • The Hirota's direct method for multiple-soliton solutions for three model equations of shallow water waves
    • Wazwaz A.M. The Hirota's direct method for multiple-soliton solutions for three model equations of shallow water waves. Appl. Math. Comput. 201 1/2 (2008) 489-503
    • (2008) Appl. Math. Comput. , vol.201 , Issue.1-2 , pp. 489-503
    • Wazwaz, A.M.1
  • 30
    • 44649179317 scopus 로고    scopus 로고
    • Multiple-soliton solutions of two extended model equations for shallow water waves
    • Wazwaz A.M. Multiple-soliton solutions of two extended model equations for shallow water waves. Appl. Math. Comput. 201 1/2 (2008) 790-799
    • (2008) Appl. Math. Comput. , vol.201 , Issue.1-2 , pp. 790-799
    • Wazwaz, A.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.