PERIODIC SOLUTION TO GENERAL CONDUCTION PROBLEMS
Abstract
In this paper, we present a modified exp-function method, where hyperbolic cosine and cosine functions are used. The hyperbolic cosine functions are responsible for energy localization while cosine functions reveal the periodic effect. A general conduction problem is used as an example to illustrate the solution process.
Dates
- Submission Date2013-03-20
- Revision Date2013-04-18
- Acceptance Date2013-04-30
- Online Date2013-12-28
References
- Hirota, R., The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, UK, 2004
- Lou, S. Y., Searching For Higher Dimensional Integrable Models From Lower Ones Via Painleve Analysis, Phys Rev Lett., 80 (1998), 23, pp. 5027-5032
- Lou, S. Y., Dromions, Dromions Lattice, Breathers and Instantons of the Davey-Stewartson Equation, Physica Scripta., 65 (2002), 1, pp. 7-12
- Dai, Z. D., et al., The Three-Wave Method for Non-linear Evolution Equations, Nonl. Sci. Lett. A, 1 (2010), 2, pp. 77-82
- He, J.-H., Wu, X.-H., Exp-Function Method for Non-linear Wave Equations, Chaos, Solitons & Fractals, 30 (2006), 3, pp. 700-708
- He, J.-H., Abdou M. A., New Periodic Solutions for Non-linear Evolution Equations Using Exp-Function Method, Chaos, Solitions & Fractals, 34 (2006), 5, pp. 1421-1429
- He, J.-H., Some Asymptotic Methods for Strongly Non-linear Equations, Int. J. Mod. Phys. B, 20 (2006), 10, pp. 1141-1199
- He, J.-H., Asymptotic Methods for Solitary Solutions and Compactons, Abstract and Applied Analysis, 2012 (2012), ID 916793
- He, J.-H., An Elementary Introduction to Recently Developed Asymptotic Methods and Nanomechanics in Textile Engineering. International Journal of Modern Physics B, 22 (2008), 21, pp. 3487-3578
- Bekir, A., Painleve Test for Some (2+1)-Dimensional Non-linear Equations, Chaos, Solitons and Fractals, 32, (2007), 2, pp. 449-455
Volume
17,
Issue
5,
Pages1494 -1496