메뉴 건너뛰기




Volumn 55, Issue 6, 2008, Pages 1113-1121

Symbolic computation and new families of exact travelling solutions for the Kawahara and modified Kawahara equations

Author keywords

Exponential rational function method; Kawahara equation; Modified Kawahara equation; Tanh method; Traveling wave solutions

Indexed keywords

CODES (SYMBOLS); COMPUTATION THEORY; FUNCTIONS; PROBLEM SOLVING; SOLITONS;

EID: 38849137848     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2007.06.018     Document Type: Article
Times cited : (35)

References (45)
  • 2
    • 0035517241 scopus 로고    scopus 로고
    • Introduction to solitons
    • Wadati M. Introduction to solitons. Pramana: J. Phys. 57 5-6 (2001) 841-847
    • (2001) Pramana: J. Phys. , vol.57 , Issue.5-6 , pp. 841-847
    • Wadati, M.1
  • 3
    • 0347821899 scopus 로고
    • The exact solution of the modified Korteweg-de Vries equation
    • Wadati M. The exact solution of the modified Korteweg-de Vries equation. J. Phys. Soc. Japan 32 (1972) 1681-1687
    • (1972) J. Phys. Soc. Japan , vol.32 , pp. 1681-1687
    • Wadati, M.1
  • 4
    • 0007690397 scopus 로고
    • The modified Korteweg-de Vries equation
    • Wadati M. The modified Korteweg-de Vries equation. J. Phys. Soc. Japan 34 (1973) 1289-1296
    • (1973) J. Phys. Soc. Japan , vol.34 , pp. 1289-1296
    • Wadati, M.1
  • 6
    • 0013052570 scopus 로고
    • Direct method of finding exact solutions of nonlinear evolution equations
    • Bullough R., and Caudrey P. (Eds), Springer, Berlin
    • Hirota R. Direct method of finding exact solutions of nonlinear evolution equations. In: Bullough R., and Caudrey P. (Eds). Backlund Transformations (1980), Springer, Berlin 1157-1175
    • (1980) Backlund Transformations , pp. 1157-1175
    • Hirota, R.1
  • 7
    • 0001229736 scopus 로고
    • Solitary wave solutions of nonlinear wave equations
    • Malfliet W. Solitary wave solutions of nonlinear wave equations. Amer. J. Phys. 60 (1992) 650-654
    • (1992) Amer. J. Phys. , vol.60 , pp. 650-654
    • Malfliet, W.1
  • 8
    • 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. Physica. Scripta 54 (1996) 563-568
    • (1996) Physica. Scripta , vol.54 , pp. 563-568
    • Malfliet, W.1    Hereman, W.2
  • 9
    • 0034606149 scopus 로고    scopus 로고
    • Extented tanh-function method and its applications to nonlinear equations
    • Fan E. Extented tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277 (2000) 212
    • (2000) Phys. Lett. A , vol.277 , pp. 212
    • Fan, E.1
  • 10
    • 33745177020 scopus 로고    scopus 로고
    • Exp-function method for nonlinear wave equations
    • He J.-H., and Wu Xu.-H. Exp-function method for nonlinear wave equations. Chaos Solitons Fractals 30 (2006) 700-708
    • (2006) Chaos Solitons Fractals , vol.30 , pp. 700-708
    • He, J.-H.1    Wu, Xu.-H.2
  • 11
    • 34250163508 scopus 로고    scopus 로고
    • New periodic solutions for nonlinear evolution equations using Exp-function method
    • He J.H., and Abdou M.A. New periodic solutions for nonlinear evolution equations using Exp-function method. Chaos Solitons Fractals 34 5 (2007) 1421-1429
    • (2007) Chaos Solitons Fractals , vol.34 , Issue.5 , pp. 1421-1429
    • He, J.H.1    Abdou, M.A.2
  • 12
    • 38849153144 scopus 로고    scopus 로고
    • X.H. Wu, J.-H. He, Exp-function method and its application to nonlinear equations, Chaos Solitons Fractals, in press (doi:10.1016/j.chaos.2007.01.024)
    • X.H. Wu, J.-H. He, Exp-function method and its application to nonlinear equations, Chaos Solitons Fractals, in press (doi:10.1016/j.chaos.2007.01.024)
  • 13
    • 20844437798 scopus 로고    scopus 로고
    • The tanh and the sine-cosine methods for a reliable treatment of the modified equal width equation and its variants
    • Wazwaz A.M. The tanh and the sine-cosine methods for a reliable treatment of the modified equal width equation and its variants. Commun. Nonlinear Sci. Numer. Simul. 11 2 (2006) 148-160
    • (2006) Commun. Nonlinear Sci. Numer. Simul. , vol.11 , Issue.2 , pp. 148-160
    • Wazwaz, A.M.1
  • 14
    • 27944503380 scopus 로고    scopus 로고
    • The tanh method and the sine-cosine method for solving the KP-MEW equation
    • Wazwaz A.M. The tanh method and the sine-cosine method for solving the KP-MEW equation. Int. J. Comput. Math. 82 2 (2005) 235-246
    • (2005) Int. J. Comput. Math. , vol.82 , Issue.2 , pp. 235-246
    • Wazwaz, A.M.1
  • 15
    • 4344673183 scopus 로고    scopus 로고
    • A note on the homogeneous balance method
    • Fan E., and Zhang H. A note on the homogeneous balance method. Phys. Lett. A 246 (1998) 403-406
    • (1998) Phys. Lett. A , vol.246 , pp. 403-406
    • Fan, E.1    Zhang, H.2
  • 16
    • 0035888417 scopus 로고    scopus 로고
    • On the extented applications of homogeneous balance method
    • Senthilvelan M. On the extented applications of homogeneous balance method. Appl. Math. Comput. 123 (2001) 381-388
    • (2001) Appl. Math. Comput. , vol.123 , pp. 381-388
    • Senthilvelan, M.1
  • 17
    • 0001051423 scopus 로고    scopus 로고
    • Exact solutions for a compound KdV-Burgers equation
    • Wang M.L. Exact solutions for a compound KdV-Burgers equation. Phys. Lett. A 213 (1996) 279-287
    • (1996) Phys. Lett. A , vol.213 , pp. 279-287
    • Wang, M.L.1
  • 18
    • 12044253199 scopus 로고
    • Compactons: Solitons with finite wavelengths
    • Rosenau P., and Hyman J.M. Compactons: Solitons with finite wavelengths. Phys. Rev. Lett. 70 5 (1993) 564-567
    • (1993) Phys. Rev. Lett. , vol.70 , Issue.5 , pp. 564-567
    • Rosenau, P.1    Hyman, J.M.2
  • 19
    • 0008071969 scopus 로고    scopus 로고
    • Lie Symmetries, Kac-Moody-Virasoro algebras and integrability of certain (2 + 1)-dimensional nonlinear evolution equations
    • Senthilvelan M., and Laksmanan M. Lie Symmetries, Kac-Moody-Virasoro algebras and integrability of certain (2 + 1)-dimensional nonlinear evolution equations. J. Nonlinear Math. Phys. 5 (1998) 190-211
    • (1998) J. Nonlinear Math. Phys. , vol.5 , pp. 190-211
    • Senthilvelan, M.1    Laksmanan, M.2
  • 20
    • 0032672778 scopus 로고    scopus 로고
    • Homotopy perturbation technique
    • He J.-H. Homotopy perturbation technique. Comput. Methods Appl. Mech. Engrg. 178 3-4 (1999) 257-262
    • (1999) Comput. Methods Appl. Mech. Engrg. , vol.178 , Issue.3-4 , pp. 257-262
    • He, J.-H.1
  • 21
    • 0033702384 scopus 로고    scopus 로고
    • A coupling method of homotopy technique and perturbation technique for nonlinear problems
    • He J.-H. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int. J. Nonlinear Mech. 35 1 (2000) 37-43
    • (2000) Int. J. Nonlinear Mech. , vol.35 , Issue.1 , pp. 37-43
    • He, J.-H.1
  • 22
    • 17844387391 scopus 로고    scopus 로고
    • Homotopy perturbation method for bifurcation of nonlinear problems
    • He J.-H. Homotopy perturbation method for bifurcation of nonlinear problems. Int. J. Nonlinear Sci. Numer. Simul. 6 2 (2005) 207
    • (2005) Int. J. Nonlinear Sci. Numer. Simul. , vol.6 , Issue.2 , pp. 207
    • He, J.-H.1
  • 23
    • 34548459893 scopus 로고    scopus 로고
    • E. Yusufoglu, An efficient algorithm for solving integro-differential equations system, Appl. Math. Comput., in press (doi:10.1016/j.amc.2007.02.134)
    • E. Yusufoglu, An efficient algorithm for solving integro-differential equations system, Appl. Math. Comput., in press (doi:10.1016/j.amc.2007.02.134)
  • 24
    • 34548580632 scopus 로고    scopus 로고
    • E. Yusufoglu, Homotopy perturbation method for solving a nonlinear system of second order boundary value problems, Int. J. Nonlinear Sci. Numer. Simul. 8 (3) 353-358
    • E. Yusufoglu, Homotopy perturbation method for solving a nonlinear system of second order boundary value problems, Int. J. Nonlinear Sci. Numer. Simul. 8 (3) 353-358
  • 25
    • 0032307661 scopus 로고    scopus 로고
    • Approximate analytical solution for seepage flow with fractional derivatives in porous media
    • He J.-H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Methods Appl. Mech. Engrg. 167 (1998) 57
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.167 , pp. 57
    • He, J.-H.1
  • 26
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equations
    • He J.-H. Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 20 10 (2006) 1141-1199
    • (2006) Int. J. Mod. Phys. B , vol.20 , Issue.10 , pp. 1141-1199
    • He, J.-H.1
  • 27
    • 34249883978 scopus 로고    scopus 로고
    • Variational iteration method for construction of some compact and noncompact structures of Klein-Gordon equations
    • Yusufoglu E. Variational iteration method for construction of some compact and noncompact structures of Klein-Gordon equations. Int. J. Nonlinear Sci. Numer. Simul. 8 2 (2007) 153-158
    • (2007) Int. J. Nonlinear Sci. Numer. Simul. , vol.8 , Issue.2 , pp. 153-158
    • Yusufoglu, E.1
  • 28
    • 34447636239 scopus 로고    scopus 로고
    • The variational iteration method for solitary patterns solutions of gBBM equation
    • Yusufoglu E., and Bekir A. The variational iteration method for solitary patterns solutions of gBBM equation. Phys. Lett. A 367 (2007) 461-464
    • (2007) Phys. Lett. A , vol.367 , pp. 461-464
    • Yusufoglu, E.1    Bekir, A.2
  • 29
    • 0038451356 scopus 로고    scopus 로고
    • New exact travelling wave solutions for the Kawahara and modified Kawahara equations
    • Sirendaoreji. New exact travelling wave solutions for the Kawahara and modified Kawahara equations. Chaos Solitons Fractals 19 (2004) 147-150
    • (2004) Chaos Solitons Fractals , vol.19 , pp. 147-150
    • Sirendaoreji1
  • 30
    • 18444384233 scopus 로고    scopus 로고
    • Doubly periodic solutions of the modified Kawahara equations
    • Zhang D. Doubly periodic solutions of the modified Kawahara equations. Chaos Solitons Fractals 25 (2005) 1155-1160
    • (2005) Chaos Solitons Fractals , vol.25 , pp. 1155-1160
    • Zhang, D.1
  • 31
    • 0037697149 scopus 로고    scopus 로고
    • Compacton solutions of the Kawahara-type nonlinear dispersive equation
    • Wazwaz A.M. Compacton solutions of the Kawahara-type nonlinear dispersive equation. Appl. Math. Comput. 145 (2003) 133-150
    • (2003) Appl. Math. Comput. , vol.145 , pp. 133-150
    • Wazwaz, A.M.1
  • 32
    • 38849179648 scopus 로고    scopus 로고
    • Existence and uniqueness of solutions to nonlinear Kawahara equations
    • Shuangping T., and Shuangbin C. Existence and uniqueness of solutions to nonlinear Kawahara equations. Chinese Ann. Math. Ser. A 23 2 (2002) 221-228
    • (2002) Chinese Ann. Math. Ser. A , vol.23 , Issue.2 , pp. 221-228
    • Shuangping, T.1    Shuangbin, C.2
  • 33
    • 77952762814 scopus 로고
    • Oscillatory solitary waves in dispersive media
    • Kawahara T. Oscillatory solitary waves in dispersive media. J. Phys. Soc. Japan 33 (1972) 260
    • (1972) J. Phys. Soc. Japan , vol.33 , pp. 260
    • Kawahara, T.1
  • 34
    • 0001472555 scopus 로고
    • Weakly non-local solitons for capillary-gravity waves: Fifth degree KdV equation
    • Boyd J.P. Weakly non-local solitons for capillary-gravity waves: Fifth degree KdV equation. Physica D 48 (1991) 129-146
    • (1991) Physica D , vol.48 , pp. 129-146
    • Boyd, J.P.1
  • 35
    • 0000219244 scopus 로고
    • Existence of perturbed solitary wave solutions to a model equation for water waves
    • Hunter J.K., and Scheule J. Existence of perturbed solitary wave solutions to a model equation for water waves. Physica D 32 (1988) 253-268
    • (1988) Physica D , vol.32 , pp. 253-268
    • Hunter, J.K.1    Scheule, J.2
  • 36
    • 0036692551 scopus 로고    scopus 로고
    • Generalized tanh method extented to special types of nonlinear equations
    • Fan E., and Hon Y.C. Generalized tanh method extented to special types of nonlinear equations. Z. Naturforsch 57a (2002) 692-700
    • (2002) Z. Naturforsch , vol.57 a , pp. 692-700
    • Fan, E.1    Hon, Y.C.2
  • 38
    • 17844375694 scopus 로고    scopus 로고
    • New exact solutions for (3 + 1)-dimensional kadomtsev- petviashvili equation and generalized (2 + 1)-dimensional boussinesq equation
    • El-Sabbagh M.F., and Ali A.T. New exact solutions for (3 + 1)-dimensional kadomtsev- petviashvili equation and generalized (2 + 1)-dimensional boussinesq equation. Int. J. Nonlinear Sci. Numer. Simul. 6 (2005) 151-162
    • (2005) Int. J. Nonlinear Sci. Numer. Simul. , vol.6 , pp. 151-162
    • El-Sabbagh, M.F.1    Ali, A.T.2
  • 39
    • 37549036955 scopus 로고    scopus 로고
    • E. Yusufoglu, A. Bekir, Exact solutions of coupled nonlinear evolution equations, Chaos Solitons Fractals, in press (doi:10.1016/j.chaos.2006.09.074)
    • E. Yusufoglu, A. Bekir, Exact solutions of coupled nonlinear evolution equations, Chaos Solitons Fractals, in press (doi:10.1016/j.chaos.2006.09.074)
  • 40
    • 38849161749 scopus 로고    scopus 로고
    • E. Yusufoglu, A. Bekir, M. Alp, The tanh and the sine-cosine methods for exact solutions of the MBBM and the Vakhnenko equations, Chaos Solitons Fractals, in press (doi:10.1016/j.chaos.2007.02.004)
    • E. Yusufoglu, A. Bekir, M. Alp, The tanh and the sine-cosine methods for exact solutions of the MBBM and the Vakhnenko equations, Chaos Solitons Fractals, in press (doi:10.1016/j.chaos.2007.02.004)
  • 41
    • 25144450080 scopus 로고    scopus 로고
    • The tanh method: Exact solutions of the Sine-Gordon and Sinh-Gordon equations
    • Wazwaz A.M. The tanh method: Exact solutions of the Sine-Gordon and Sinh-Gordon equations. Appl. Math. Comput. 167 (2005) 1196-1210
    • (2005) Appl. Math. Comput. , vol.167 , pp. 1196-1210
    • Wazwaz, A.M.1
  • 42
    • 34247350849 scopus 로고    scopus 로고
    • Application of Exp-function method to a KdV equation with variable coefficients
    • Zhang S. Application of Exp-function method to a KdV equation with variable coefficients. Phys. Lett. A 365 5-6 (2007) 448-453
    • (2007) Phys. Lett. A , vol.365 , Issue.5-6 , pp. 448-453
    • Zhang, S.1
  • 43
    • 38849119316 scopus 로고    scopus 로고
    • S. Zhang, Application of Exp-function method to high-dimensional nonlinear evolution equations, Chaos Solitons Fractals, in press (doi:10.1016/j.chaos.2006.11.014)
    • S. Zhang, Application of Exp-function method to high-dimensional nonlinear evolution equations, Chaos Solitons Fractals, in press (doi:10.1016/j.chaos.2006.11.014)
  • 44
    • 34147152832 scopus 로고    scopus 로고
    • Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method
    • Ebaid A. Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method. Phys. Lett. A 365 3 (2007) 213-219
    • (2007) Phys. Lett. A , vol.365 , Issue.3 , pp. 213-219
    • Ebaid, A.1
  • 45
    • 3042713895 scopus 로고    scopus 로고
    • A travelling wave solution to the Korteweg-de Vries-Burger equation
    • Demiray H. A travelling wave solution to the Korteweg-de Vries-Burger equation. Appl. Math. Comput. 154 (2004) 665-670
    • (2004) Appl. Math. Comput. , vol.154 , pp. 665-670
    • Demiray, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.