Traveling Wave Solutions of the RLW and Boussinesq Equations
Year 2014,
Volume: 2 Issue: 2, 69 - 77, 01.08.2014
Yavuz Uğurlu
Doğan Kaya
İbrahim Enam İnan
Abstract
In this study, we use the generalized tanh function method for the traveling wave solutions of the generalized regularized long-wave (gRLW) equation and Boussinesq equation system
References
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- Lou S., Huang G., Ruan H. Exact solitary waves in a convecting fluid. J. Phys. A: Math. Gen. 24 (1991) L587-L590.
- Malfliet W. Solitary wave solutions of nonlinear wave equations, Am. J. Phys. 60 (1992) p.650-654.
- Parkes E. J., Duffy B. R. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations. Comput. Phys. Commun. 98 (1996) p.288-300.
- Fan E. Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277 (2000) p.212-218.
- Elwakil S. A., El-labany S. K., Zahran M. A., Sabry R. Modified extended tanh-function method for solving nonlinear partial differential equations. Phys. Lett. A 299 (2002) p.179-188.
- Zheng X., Chen Y., Zhang H. Generalized extended tanh-function method and its application to (1+1)-dimensional dispersive long wave equation. Phys. Lett. A 311 (2003) p.145-157.
- Yomba E. Construction of new soliton-like solutions of the (2+1) dimensional dispersive long wave equation. Chaos Solitons Fract. 20 (2004) p.1135-1139.
- Chen H., Zhang H. New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation. Chaos Solitons Fract.19 (2004) p.71-76.
- Chen H., Zhang H. New multiple soliton-like solutions to the generalized (2 + 1)-dimensional KP equation. Appl. Math. and Comput. 157 (2004) p.765-773.
- Peregrine D.H. Calculations of the development of an undular bore. J. Fluid Mech. 25 (1996) p.321-330.
- Peregrine D.H. Long waves on a beach,.J. Fluid Mech. 27 (1967) p.815-827.
- Benjamin T.B., Bona J.L., Mahony J.J. Model equations for long waves in non-linear dispersive systems. Phil. Trans. of the Royal Soc. 272A (1972) p.47-78.
- Bona J.L., Pritchard W.G., Scott L.R.. A comparison of solutions of two model equations for long waves, in: N.R. Lebovitz (Ed.), Fluid Dynamics in Astrophysics and Geophysics, Lectures in Appl. Math. (1983) p.235–267.
- Bona J.L., Pritchard W.G., Scott L.R. An evaluation of a model equation for water waves. Phil. Trans. of the Royal Soc. 302 A (1981) 457- 5
- Sachs R.L. On the integrable variant of the boussinesq system: Painlevé property, rational solutions, a related many-body system, and equivalence with the AKNS hierarchy. Physica D 30 (1988) p.1-27.
Traveling Wave Solutions of the RLW and Boussinesq Equations
Year 2014,
Volume: 2 Issue: 2, 69 - 77, 01.08.2014
Yavuz Uğurlu
Doğan Kaya
İbrahim Enam İnan
References
- Debtnath L. Nonlinear Partial Differential Equations for Scientist and Engineers. Birkhauser, Boston, MA, 1997.
- Wazwaz A.M. Partial Differential Equations: Methods and Applications. Balkema, Rotterdam, 2002.
- Hereman W., Banerjee P.P., Korpel A., Assanto G., Immerzeele A. van, Meerpoel A. Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method. J. Phys. A: Math. Gen. 19 (1986) p. 607-628.
- Khater A.H., Helal M.A., El-Kalaawy O.H. Bäcklund transformations: exact solutions for the KdV and the Calogero-Degasperis-Fokas mKdV equations. Math. Meth. in the Appl. Sci. 21 (1998) p.719-731.
- Khater A.H., Malfiet W., Kamel E.S. Travelling wave solutions of some classes of nonlinear evolution equations in (1+1) and higher dimensions. Math. Comput. Simul 64 (2004) p.247-258.
- M. Inc. Constructing solitary pattern solutions of the nonlinear dispersive Zakharov–Kuznetsov equation. Chaos Solitons Fract. 39 (2009) p.109-119.
- Khater A.H., Hassan M.M., Temsah R.S. Cnoidal wave solutions for a class of fifth-order KdV equations. Math. Comput. Simul. 70 (2005) p.221-226.
- Ugurlu Y., Kaya D. Solutions the Cahn-Hilliard Equation. Comput. & Math. with Appl. 56 (2008) p.3038-3045.
- Khater A.H., Callebaut D.K., Seadawy A.R. General soliton solutions of an n-dimensional complex Ginzberg-Landau equation. Phys. Scr. 62 (2000) p.353-357.
- Khater A.H., Hassan M.M., Temsah R.S. Exact solutions with Jacobi elliptic functions of two nonlinear models for ion acoustic plasma wave. J. Phys. Soc. Japan 74 (2005) p1431-1435.
- Inan I.E. Exact solutions for coupled KdV equation and KdV equations. Phys. Lett. A 371 (2007) p.90-95.
- Oziş T., Yıldırım A. Reliable analysis for obtaining exact soliton solutions of nonlinear Schrödinger (NLS) equation. Chaos Solitons Fract. 38 (2008), p. 209-212.
- M. Inc. An L-stable extended two-step method for the integration of ordinary differential equations. Appl. Math. Comput. 186 (2007) 1395- 140
- M. Inc. An approximate solitary wave solution with compact support for the modified KdV equation. Appl. Math. Comput. 184 (2007) p.631-637.
- Uğurlu Y., Kaya D. Exact and Numerical Solutions of Generalized Drinfeld-Sokolov Equations. Phys. Lett. A 372 (2008) p.2876-2873.
- Fan E.G. Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277 (2000) p.212-218.
- Chen H., Zhang H. New multiple soliton solutions to the general Burgers–Fisher equation and the Kuramoto–Sivashinsky equation. Chaos Solitons Fract. 19 (2004) p.71-76.
- Hereman W., Korpel A., Banerjee P.P. Wave Motion 7 (1985) p.283-289.
- Hereman W., Takaoka M. Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA. J. Phys. A: Math. Gen. 23 (1990) p.4805-4822.
- Lan H., Wang K. Exact solutions for two nonlinear equations. J. Phys. A: Math. Gen. 23 (1990) p.3923-3928.
- Lou S., Huang G., Ruan H. Exact solitary waves in a convecting fluid. J. Phys. A: Math. Gen. 24 (1991) L587-L590.
- Malfliet W. Solitary wave solutions of nonlinear wave equations, Am. J. Phys. 60 (1992) p.650-654.
- Parkes E. J., Duffy B. R. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations. Comput. Phys. Commun. 98 (1996) p.288-300.
- Fan E. Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277 (2000) p.212-218.
- Elwakil S. A., El-labany S. K., Zahran M. A., Sabry R. Modified extended tanh-function method for solving nonlinear partial differential equations. Phys. Lett. A 299 (2002) p.179-188.
- Zheng X., Chen Y., Zhang H. Generalized extended tanh-function method and its application to (1+1)-dimensional dispersive long wave equation. Phys. Lett. A 311 (2003) p.145-157.
- Yomba E. Construction of new soliton-like solutions of the (2+1) dimensional dispersive long wave equation. Chaos Solitons Fract. 20 (2004) p.1135-1139.
- Chen H., Zhang H. New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation. Chaos Solitons Fract.19 (2004) p.71-76.
- Chen H., Zhang H. New multiple soliton-like solutions to the generalized (2 + 1)-dimensional KP equation. Appl. Math. and Comput. 157 (2004) p.765-773.
- Peregrine D.H. Calculations of the development of an undular bore. J. Fluid Mech. 25 (1996) p.321-330.
- Peregrine D.H. Long waves on a beach,.J. Fluid Mech. 27 (1967) p.815-827.
- Benjamin T.B., Bona J.L., Mahony J.J. Model equations for long waves in non-linear dispersive systems. Phil. Trans. of the Royal Soc. 272A (1972) p.47-78.
- Bona J.L., Pritchard W.G., Scott L.R.. A comparison of solutions of two model equations for long waves, in: N.R. Lebovitz (Ed.), Fluid Dynamics in Astrophysics and Geophysics, Lectures in Appl. Math. (1983) p.235–267.
- Bona J.L., Pritchard W.G., Scott L.R. An evaluation of a model equation for water waves. Phil. Trans. of the Royal Soc. 302 A (1981) 457- 5
- Sachs R.L. On the integrable variant of the boussinesq system: Painlevé property, rational solutions, a related many-body system, and equivalence with the AKNS hierarchy. Physica D 30 (1988) p.1-27.