Proceedings of the Sixth International Conference on Management Science and Engineering Management pp 139-148 | Cite as

# Solutions of Modified Equal Width Equation by Means of the Auxiliary Equation with a Sixth-Degree Nonlinear Term

Conference paper

First Online:

## Abstract

In this paper, by means of symbolic computation, the new solutions of original auxiliary equation of first-order nonlinear ordinary differential equation with sixth-degree nonlinear term are presented to obtain novel exact solutions of the modified equal width equation. By the aid of the solutions of the original auxiliary equation; some other physically important nonlinear equations can be solved to construct novel exact solutions.

### Keywords

Nonlinear equations Symbolic computation Auxiliary equation method Modified equal width equation Wave solutions## Preview

Unable to display preview. Download preview PDF.

### References

- 1.Yong C, Biao L, Hong-Quing Z (2003) Generalized Riccati equation expansion method and its application to Bogoyaylenskii’s generalized breaking soliton equation. Chinese Physics 12:940–946Google Scholar
- 2.Zhou Y, Wang M, Wang Y (2003) Periodic wave solutions to a coupled KdV equations with variable coefficient. Physics Letters A 308:31–36Google Scholar
- 3.Cai G,Wang Q, Huang J (2006) A modified F-expansion method for solving breaking soliton equation. International Journal of Nonlinear science 2:122–128Google Scholar
- 4.Zeng X, Yong X (2008) A new mapping method and its applications to nonlinear partial differential equations. Physics Letters A 372:6602–6607Google Scholar
- 5.Yong X, Zeng X, Zhang Z et al. (2009) Symbolic computation of Jacobi elliptic function solutions to nonlinear differential-difference equations. Computers & Mathematics with Applications 57:1107–1114Google Scholar
- 6.O¨ zis T, Aslan I (2008) Exact and explicit solutions to the (3 + 1)-dimensional Jimbo-Miwa equation via the Exp-function method. Physics Letters A 372:7011–7015Google Scholar
- 7.Ozis T, Koroglu C (2008) A novel approach for solving the Fisher equation using Expfunction method. Physics Letters A 372:3836–3840Google Scholar
- 8.Yildirim A, Pinar Z (2010) Application of the exp-function method for solving nonlinear reaction diffusion equations arising in mathematical biology. Computers & Mathematics with Applications 60:1873–1880Google Scholar
- 9.Ma WX, Huang T, Zhang Y (2010) A multiple Exp-function method for nonlinear differential equations and its applications. Physica Scripta 82(065003)8–8Google Scholar
- 10.Ozis T, Aslan I (2010) Application of the G’/G-expansion method to Kawahara type equations using symbolic computation. Applied Mathematics and Computation 216:2360–2365Google Scholar
- 11.Ozis T, Aslan I (2009) Symbolic computation and construction of new exact traveling wave solutions to Fitzhugh-Nagumo and Klein Gordon equation. Zeitschrift f¨ur Naturforschung-A 64:15–20Google Scholar
- 12.Aslan I, Ozis T (2009) an analytical study on nonlinear evolution equations by using the (G’/G)-expansion method. Applied Mathematics and Computation 209:425–429Google Scholar
- 13.Ozis T, Aslan I (2009) Symbolic computations and exact and explicit solutions of some nonlinear evolution equations in mathematical physics. Communications in Theoretical Physics 51:577–580Google Scholar
- 14.Zhang H (2009) A note on some sub-equation methods and new types of exact travelling wave solutions for two nonlinear partial differential equations. Acta Applicandae Mathematicae 106:241–249Google Scholar
- 15.Lia B, Chena Y, Lia YQ (2008) A generalized sub-equation expansion method and some analytical solutions to the inhomogeneous higher-order nonlinear schr¨odinger equation. Zeitschrift f¨ur Naturforschung 63:763–777Google Scholar
- 16.Yomba E (2006) The modified extended Fan sub-equation method and its application to the (2 + 1)-dimensional Broer-Kaup-Kupershmidt equation. Chaos Solitons Fractals 27:187–196Google Scholar
- 17.Wu GJ, Han JH, Wen-Liang Z et al. (2007) New periodic wave solutions to generalized Klein Gordon and Benjamin equations. Communications in Theoretical Physics 48:815–818Google Scholar
- 18.Sirendaoreji S (2007) Auxiliary equation method and new solutions of Klein-Gordon equations. Chaos, Solitons and Fractals 31:943–950Google Scholar
- 19.Jang B (2009) New exact travelling wave solutions of nonlinear Klein-Gordon equations. Chaos, Solitons and Fractals 41:646–654Google Scholar
- 20.Lv X, Lai S, Wu YH (2009) An auxiliary equation technique and exact solutions for a nonlinear Klein-Gordon equation. Chaos, Solitons and Fractals 41:82–90Google Scholar
- 21.Yomba E (2008) A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations. Physics Letters A 372:1048–1060Google Scholar
- 22.Wazwaz AM (2006) The tanh and the sine-cosine methods for a reliable treatment of the modified equal width equation and its variants. Communications in Nonlinear Science and Numerical Simulation 11:148–160Google Scholar
- 23.Zaki SI (2000) A least-squares Finite element scheme for the EW equation. Computer Methods in Applied Mechanics and Engineering 189:587–594Google Scholar
- 24.Morrison PJ, Meiss JD, Carey JR (1981) Scattering of RLW solitary waves. Physica 11:324-36Google Scholar
- 25.Peregrine DH (1966) Calculations of the development of an undular bore. Journal of Fluid Mechanics 25:321–330Google Scholar
- 26.Peregrine DH (1967) Long waves on a beach. Journal of Fluid Mechanics 27:815–827Google Scholar
- 27.Benjamin TB, Bona JL, Mahony JJ (1972) Model equations for waves in nonlinear dispersive systems. Philosophical Transactions of the Royal Society of London 227:47–48Google Scholar
- 28.Kaya D (2004) A numerical simulation of solitary-wave solutions of the generalized longwave equation. Applied Mathematics and Computation 149:833–841Google Scholar
- 29.Kaya D, El-Sayed SM (2003) An application of the decomposition method for the generalized KdV and RLW equations. Chaos, Solitons and Fractals 17:869–877Google Scholar
- 30.Bona JL, Pritchard WG, Scott LR (1983) A comparison of solutions of two model equations for long waves. NASA STI/Recon Technical Report N 83:34–38Google Scholar
- 31.Bona JL, Pritchard WG, Scott LR (1981) An evaluation for water waves. Philosophical Transactions of the Royal Society of London 302:457–510Google Scholar

## Copyright information

© Springer-Verlag London 2013