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2015 | OriginalPaper | Chapter

Exact Solutions and Conservation Laws of the Joseph-Egri Equation with Power Law Nonlinearity

Authors : Abdullahi Rashid Adem, Chaudry Masood Khalique

Published in: Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Publisher: Springer International Publishing

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Abstract

In this chapter we obtain exact solutions of the Joseph-Egri equation with power law nonlinearity, which arises in various problems in many scientific applications. The Lie group analysis and simplest equation method are used to carry out the integration of this equation. The solutions obtained are travelling wave solutions. Moreover, the conservation laws for the Joseph-Egri equation with power law nonlinearity are constructed by using the multiplier method.

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Literature
1.
go back to reference Adem, A.R., Khalique, C.M.: Symmetry reductions, exact solutions and conservationlaws of a new coupled KdV system. Commun. Nonlinear Sci. Numer. Simul. 17, 3465–3475 (2012)MATHMathSciNetCrossRef Adem, A.R., Khalique, C.M.: Symmetry reductions, exact solutions and conservationlaws of a new coupled KdV system. Commun. Nonlinear Sci. Numer. Simul. 17, 3465–3475 (2012)MATHMathSciNetCrossRef
2.
go back to reference Anco, S.C., Bluman, G.W.: Direct construction method for conservation laws of partial differential equations. Part I: examples of conservation law classifications. Eur. J. Appl. Math. 13, 545–566 (2002)MATHMathSciNet Anco, S.C., Bluman, G.W.: Direct construction method for conservation laws of partial differential equations. Part I: examples of conservation law classifications. Eur. J. Appl. Math. 13, 545–566 (2002)MATHMathSciNet
3.
go back to reference Anthonyrajah, M., Mason, D.P.: Conservation laws and invariant solutions in the Fanno model for turbulent compressible flow. Math. Comput. Appl. 15, 529–542 (2010)MATHMathSciNet Anthonyrajah, M., Mason, D.P.: Conservation laws and invariant solutions in the Fanno model for turbulent compressible flow. Math. Comput. Appl. 15, 529–542 (2010)MATHMathSciNet
4.
go back to reference Hereman, W., Banerjee, P.P., Korpel, A., Assanto, G., van Immerzeele, A., Meerpole, A.: Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method. J. Phys. A. Math. Gen. 1, 607–628 (1986)CrossRef Hereman, W., Banerjee, P.P., Korpel, A., Assanto, G., van Immerzeele, A., Meerpole, A.: Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method. J. Phys. A. Math. Gen. 1, 607–628 (1986)CrossRef
5.
go back to reference Ibragimov, N.H.: CRC Handbook of Lie Group Analysis of Differential Equations, vols. 1–3, CRC Press, Boca Raton (1994–1996) Ibragimov, N.H.: CRC Handbook of Lie Group Analysis of Differential Equations, vols. 1–3, CRC Press, Boca Raton (1994–1996)
6.
go back to reference Kudryashov, N.A.: Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos Solitons Fractals 24, 1217–1231 (2005)MATHMathSciNetCrossRef Kudryashov, N.A.: Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos Solitons Fractals 24, 1217–1231 (2005)MATHMathSciNetCrossRef
7.
go back to reference Olver, P.J.: Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics, 107, 2nd edn. Springer-Verlag, Berlin (1993)CrossRef Olver, P.J.: Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics, 107, 2nd edn. Springer-Verlag, Berlin (1993)CrossRef
8.
go back to reference Taghizadeh, N., Mirzazadeh, M.: The multisoliton solutions of some nonlinear partial differential equations. Appl. Appl. Math. 6, 284–291 (2011)MATH Taghizadeh, N., Mirzazadeh, M.: The multisoliton solutions of some nonlinear partial differential equations. Appl. Appl. Math. 6, 284–291 (2011)MATH
Metadata
Title
Exact Solutions and Conservation Laws of the Joseph-Egri Equation with Power Law Nonlinearity
Authors
Abdullahi Rashid Adem
Chaudry Masood Khalique
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-12307-3_1

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