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Volumn 217, Issue 4, 2010, Pages 1632-1638

New exact solutions to some variable coefficients problems

Author keywords

An extended tanh method; Equations with variable coefficients; Periodic solution; Soliton wave solution; Symbolic computation

Indexed keywords

PERIODIC SOLUTION; SOLITON WAVE SOLUTION; SYMBOLIC COMPUTATION; TANH METHOD; VARIABLE COEFFICIENTS;

EID: 77957259830     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.08.055     Document Type: Article
Times cited : (4)

References (28)
  • 2
    • 0007084664 scopus 로고    scopus 로고
    • New method for explicit solution of the variable coefficient nonlinear evolution equation
    • H.Y. Ruan, and Y.X. Chen New method for explicit solution of the variable coefficient nonlinear evolution equation Acta Phys. Sin. 49 2 2000 177 180
    • (2000) Acta Phys. Sin. , vol.49 , Issue.2 , pp. 177-180
    • Ruan, H.Y.1    Chen, Y.X.2
  • 3
    • 0034204091 scopus 로고    scopus 로고
    • Similarity reductions for (2+1)-dimensional variable coefficient generalized Kadomtsev-Petviashvili equation
    • Z.Y. Yan, and H.Q. Zhang Similarity reductions for (2 + 1 ) -dimensional variable coefficient generalized Kadomtsev-Petviashvili equation Appl. Math. Mech. 21 6 2000 645 650
    • (2000) Appl. Math. Mech. , vol.21 , Issue.6 , pp. 645-650
    • Yan, Z.Y.1    Zhang, H.Q.2
  • 4
    • 31244434345 scopus 로고    scopus 로고
    • Truncated expansion method and the new solutions to the generalized KdV equation
    • J.F. Zhang, and F.Y. Chen Truncated expansion method and the new solutions to the generalized KdV equation Acta Phys. Sin. 50 9 2001 1648 1656
    • (2001) Acta Phys. Sin. , vol.50 , Issue.9 , pp. 1648-1656
    • Zhang, J.F.1    Chen, F.Y.2
  • 5
    • 0348247007 scopus 로고    scopus 로고
    • Jacobi elliptic function expansion solution to the variable coefficient nonlinear equations
    • S.K. Liu, Z.T. Fu, and S.D. Liu Jacobi elliptic function expansion solution to the variable coefficient nonlinear equations Acta Phys. Sin. 51 9 2002 1923 1926
    • (2002) Acta Phys. Sin. , vol.51 , Issue.9 , pp. 1923-1926
    • Liu, S.K.1    Fu, Z.T.2    Liu, S.D.3
  • 6
    • 33846096774 scopus 로고    scopus 로고
    • The Jacobi elliptic function-like exact solutions to two kinds of KdV equations with variable coefficients and KdV equation with forcible term
    • DOI 10.1088/1009-1963/15/12/008, 008
    • Taogetusang, and Sirendaoerji The Jacobi elliptic function-like exact solutions to two kinds of KdV equations with variable coefficients and KdV equation with forcible term Chin. Phys. 15 2006 2809 2818 (Pubitemid 46070062)
    • (2006) Chinese Physics , vol.15 , Issue.12 , pp. 2809-2818
    • Taogetusang1    Sirendaoerji2
  • 7
    • 70349199880 scopus 로고    scopus 로고
    • Solitary wave solution of the KdV equation with power-law nonlinearity and time-dependent coefficients
    • A. Biswas, Solitary wave solution of the KdV equation with power-law nonlinearity and time-dependent coefficients, Nonlinear Dyn. (2009) doi:10.1007/s11071-009-9480-5.
    • (2009) Nonlinear Dyn.
    • Biswas, A.1
  • 8
    • 27144553113 scopus 로고    scopus 로고
    • The tanh method for generalized forms of nonlinear heat conduction and Burgers-Fisher equations
    • A.M. Wazwaz The tanh method for generalized forms of nonlinear heat conduction and Burgers-Fisher equations Appl. Math. Comput. 169 2005 321 338
    • (2005) Appl. Math. Comput. , vol.169 , pp. 321-338
    • Wazwaz, A.M.1
  • 9
    • 33947194364 scopus 로고    scopus 로고
    • New solitary wave solutions to the modified forms of Degasperis-Procesi and Camassa-Holm equations
    • DOI 10.1016/j.amc.2006.07.092, PII S0096300306009246
    • A.M. Wazwaz New solitary wave solutions to the modified forms of Degasperis-Procesi and Camassa-Holm equations Appl. Math. Comput. 186 1 2007 130 141 (Pubitemid 46435606)
    • (2007) Applied Mathematics and Computation , vol.186 , Issue.1 , pp. 130-141
    • Wazwaz, A.-M.1
  • 10
    • 34247279667 scopus 로고    scopus 로고
    • The extended tanh method for abundant solitary wave solutions of nonlinear wave equations
    • DOI 10.1016/j.amc.2006.09.013, PII S0096300306012501
    • A.M. Wazwaz The extended tanh method for abundant solitary wave solutions of nonlinear wave equations Appl. Math. Comput. 187 2007 1131 1142 (Pubitemid 46627902)
    • (2007) Applied Mathematics and Computation , vol.187 , Issue.2 , pp. 1131-1142
    • Wazwaz, A.-M.1
  • 11
    • 33846641360 scopus 로고    scopus 로고
    • The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations
    • A.M. Wazwaz The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations Appl. Math. Comput. 184 2 2007 1002 1014
    • (2007) Appl. Math. Comput. , vol.184 , Issue.2 , pp. 1002-1014
    • Wazwaz, A.M.1
  • 12
    • 34248229664 scopus 로고    scopus 로고
    • The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations
    • DOI 10.1016/j.amc.2006.11.013, PII S0096300306014998
    • A.M. Wazwaz The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations Appl. Math. Comput. 188 2007 1467 1475 (Pubitemid 46710038)
    • (2007) Applied Mathematics and Computation , vol.188 , Issue.2 , pp. 1467-1475
    • Wazwaz, A.-M.1
  • 13
    • 0036462771 scopus 로고    scopus 로고
    • New solitary-wave special solutions with compact support for the nonlinear dispersive K(m,n) equations
    • A.M. Wazwaz New solitary-wave special solutions with compact support for the nonlinear dispersive K (m, n ) equations Chaos Solitons Fract. 13 2 2002 321 330
    • (2002) Chaos Solitons Fract. , vol.13 , Issue.2 , pp. 321-330
    • Wazwaz, A.M.1
  • 14
    • 33747348716 scopus 로고    scopus 로고
    • New exact traveling wave solutions using Modified extended tanh function method
    • S.A. El-Wakil, and M.A. Abdou New exact traveling wave solutions using Modified extended tanh function method Chaos Solitons Fract. 31 2007 840 852
    • (2007) Chaos Solitons Fract. , vol.31 , pp. 840-852
    • El-Wakil, S.A.1    Abdou, M.A.2
  • 15
    • 33748447485 scopus 로고    scopus 로고
    • Modified extended tanh-function method for solving nonlinear partial differential equations
    • DOI 10.1016/j.chaos.2005.10.072, PII S0960077905010386
    • S.A. El-Wakil, and M.A. Abdou Modified extended tanh function method for solving nonlinear partial differential equations Chaos Solitons Fract. 31 2007 1256 1264 (Pubitemid 44349165)
    • (2007) Chaos, Solitons and Fractals , vol.31 , Issue.5 , pp. 1256-1264
    • El-Wakil, S.A.1    Abdou, M.A.2
  • 16
    • 33646104688 scopus 로고    scopus 로고
    • Modified extended tanh function method and its applications on nonlinear physical equations
    • M.A. Abdou, and A.A. Soliman Modified extended tanh function method and its applications on nonlinear physical equations Phys. Lett. A 353 2006 487
    • (2006) Phys. Lett. A , vol.353 , pp. 487
    • Abdou, M.A.1    Soliman, A.A.2
  • 17
    • 33750480407 scopus 로고    scopus 로고
    • New exact solutions to KdV equations with variable coefficients or forcing
    • Z.T. Fu, S.D. Liu, S.K. Liu, and Q. Zhao New exact solutions to KdV equations with variable coefficients or forcing Appl. Math. Mech. 25 2004 73 79
    • (2004) Appl. Math. Mech. , vol.25 , pp. 73-79
    • Fu, Z.T.1    Liu, S.D.2    Liu, S.K.3    Zhao, Q.4
  • 18
    • 39749091634 scopus 로고    scopus 로고
    • Exact solutions of a KdV equation with variable coefficients via Exp-function method
    • DOI 10.1007/s11071-007-9251-0
    • S. Zhang Exact solutions of a KdV equation with variable coefficients via Exp-function method Nonlinear Dyn. 52 2008 11 17 (Pubitemid 351304390)
    • (2008) Nonlinear Dynamics , vol.52 , Issue.1-2 , pp. 11-17
    • Zhang, S.1
  • 19
    • 0001213644 scopus 로고
    • Symbolic software for soliton theory
    • W. Hereman, and W. Zhuang Symbolic software for soliton theory Acta Appl. Math. 39 1995 361 378
    • (1995) Acta Appl. Math. , vol.39 , pp. 361-378
    • Hereman, W.1    Zhuang, W.2
  • 20
    • 0002004721 scopus 로고
    • Solitons, nonlinear evolution equations and inverse scattering
    • Cambridge University Press Cambridge, UK
    • M.J. Ablowitz, and P.A. Clarkson Solitons, nonlinear evolution equations and inverse scattering London Mathematical Society Lecture Notes on Mathematics vol. 149 1991 Cambridge University Press Cambridge, UK
    • (1991) London Mathematical Society Lecture Notes on Mathematics , vol.149
    • Ablowitz, M.J.1    Clarkson, P.A.2
  • 21
    • 51549090757 scopus 로고    scopus 로고
    • Construction of non-travelling wave solutions for the generalized variable-coefficient Gardner equation
    • L.H. Zhang, L.H. Dong, and L.M. Yan Construction of non-travelling wave solutions for the generalized variable-coefficient Gardner equation Appl. Math. Comput. 203 2008 784 791
    • (2008) Appl. Math. Comput. , vol.203 , pp. 784-791
    • Zhang, L.H.1    Dong, L.H.2    Yan, L.M.3
  • 22
    • 0142166467 scopus 로고    scopus 로고
    • New kinds of solutions to Gardner equation
    • Z.T. Fu, S.D. Liu, and S.K. Liu New kinds of solutions to Gardner equation Chaos Solitons Fract. 20 2004 301
    • (2004) Chaos Solitons Fract. , vol.20 , pp. 301
    • Fu, Z.T.1    Liu, S.D.2    Liu, S.K.3
  • 23
    • 34249735366 scopus 로고    scopus 로고
    • New solitons and kink solutions for the Gardner equation
    • DOI 10.1016/j.cnsns.2005.11.007, PII S1007570405001826
    • A.M. Wazwaz New soliton and kink solutions for the Gardner equation Commun. Nonlinear Sci. Numer. Simul. 12 8 2007 1395 1404 (Pubitemid 46832139)
    • (2007) Communications in Nonlinear Science and Numerical Simulation , vol.12 , Issue.8 , pp. 1395-1404
    • Wazwaz, A.-M.1
  • 24
    • 34548087067 scopus 로고    scopus 로고
    • Lax pair, Bäcklund transformation and N-soliton-like solution for a variable-coefficient Gardner equation from nonlinear lattice, plasma physics and ocean dynamics with symbolic computation
    • J. Li, T. Xu, X.H. Meng, Y.X. Zhang, H.Q. Zhang, and B. Tian Lax pair, Bäcklund transformation and N-soliton-like solution for a variable-coefficient Gardner equation from nonlinear lattice, plasma physics and ocean dynamics with symbolic computation J. Math. Anal. Appl. 336 2007 1443 1455
    • (2007) J. Math. Anal. Appl. , vol.336 , pp. 1443-1455
    • Li, J.1    Xu, T.2    Meng, X.H.3    Zhang, Y.X.4    Zhang, H.Q.5    Tian, B.6
  • 25
    • 4444245136 scopus 로고    scopus 로고
    • Exact solutions to the (2+1)-dimensional Broer-Kaup equation with variable coefficients
    • J.L. Zhang, Y.M. Wang, M.L. Wang, and Z.D. Fang Exact solutions to the (2 + 1 ) -dimensional Broer-Kaup equation with variable coefficients J. Atom. Mol. Phys. 20 2003 92 (in Chinese)
    • (2003) J. Atom. Mol. Phys. , vol.20 , pp. 92
    • Zhang, J.L.1    Wang, Y.M.2    Wang, M.L.3    Fang, Z.D.4
  • 26
    • 0031508840 scopus 로고    scopus 로고
    • Infinitely many Lax pairs and symmetry constraints of the KP equation
    • DOI 10.1063/1.532219
    • S.Y. Lou, and X.B. Hu Infinitely many Lax pairs and symmetry constraints of the KP equation J. Math. Phys. 38 1997 6401 6427 (Pubitemid 127156357)
    • (1997) Journal of Mathematical Physics , vol.38 , Issue.12 , pp. 6401-6427
    • Lou, S.-Y.1    Hu, X.-B.2
  • 27
    • 0000262859 scopus 로고
    • On the stability of solitary waves in weakly dispersing media
    • B.B. Kadomtsev, and V.I. Petviashvili On the stability of solitary waves in weakly dispersing media Sov. Phys. Dokl. 15 1970 539 541
    • (1970) Sov. Phys. Dokl. , vol.15 , pp. 539-541
    • Kadomtsev, B.B.1    Petviashvili, V.I.2
  • 28
    • 13444263651 scopus 로고    scopus 로고
    • Solitons with fission and fusion behaviors in a variable coefficient Broer-Kaup system
    • DOI 10.1016/j.chaos.2004.09.069, PII S0960077904006368
    • C.L. Zheng, and L.Q. Chen Solitons with fission and fusion behaviors in a variable coefficient Broer-Kaup system Chaos, Solitons Fract. 24 2005 1347 1351 (Pubitemid 40206062)
    • (2005) Chaos, Solitons and Fractals , vol.24 , Issue.5 , pp. 1347-1351
    • Zheng, C.-L.1    Chen, L.-Q.2


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