### Generalized Solutions of Wick-type Stochastic KdV-Burgers Equations Using Exp-Function Method

^{(*)}

*Corresponding author*

**DOI's assignment:**

*the author of the article can submit here a request for assignment of a DOI number to this resource!*

**Cost of the service: euros 10,00 (for a DOI)**

#### Abstract

Variable coefficients and Wick-type stochastic KdV-Burgers equations are researched. Exp-function method is proposed to present soliton and periodic wave solutions for variable coefficients KdV-Burgers equation. Generalized white noise functional solutions for Wick-type stochastic KdV-Burgers equations are showed via Hermite transform and white noise analysis. (PACS No.: 05.40.+-a, 02.30.Jr. )

*Copyright © 2014 Praise Worthy Prize - All rights reserved.*#### Keywords

#### Full Text:

PDF#### References

M. A. Abdou,The extended F-expansion method and its application for nonlinear evolution equations Chaos Solitons and Fractals, 31(2007), 95-104.

M. A. Abdou and A. A. Soliman, Modified extended tanh-function method and its application on nonlinear physical equations, Phys. Lett. A, 353 (2006), 487-492.

E. Benth and J. Gjerde, A remark on the equivalence between Poisson and Gaussion stochastic partial differential equations Potential Anal., 8 (1998), 179-193.

A. de Bouard and A. Debussche,On the stochastic Korteweg--de Vries equation J. Funct. Anal. 154 (1998), 215-251.

A. de Bouard and A. Debussche, , Tsutsumi Y., White noise driven Korteweg--de Vries equation J.Funct. Anal. ,169 (1999), 532-558.

A. Debussche and J. Printems,Numerical simulation of the stochastic Korteweg-de Vries equation Physica D,134 (1999), 200-226.

A. Debussche and J. Printems, Effect of a localized random forcing term on the Korteweg-de Vries equation J. Comput. Anal. Appl., 3 (2001), 183-206.

D. D. Ganji and A. Sadighi, Application of He's homotopy perturbation method to nonlinear coupled systems of reaction-diffusion equations, Int J Non Sci Numer Simul, 7 (2006), 411-418.

G. Gao, A theory of interaction between dissipation and dispersion of turbulence, Sci. Sin. Ser. A, 28 (1985), 616-627.

H. A. Ghany, Eaxt solutions for stochastic generalized Hirota-Satsuma coupled KdV equations, Chin. J. Phys., 49 (2011), 926-940.

H. A. Ghany, Exact solutions for KdV-Burger Equations with an application of white-noise analysis International Journal of pure and applied mathematics, 78(2012),17-27.

H. A. Ghany and A. Hyder, White Noise Functional Solutions for the Wick-Type Two-Dimensional Stochastic Zakharov-Kuznetsov Equations International Review of Physics, 6 (2012), 153-157.

H. A. Ghany and A. Hyder, Local and global well-posedness of stochastic Zakharov-Kuznetsov equation J. Comput. Anal. Appl., 15 (2013), 1332-1343.

H. A. Ghany and A. Hyder, Exact solutions for the wick-type stochastic Time-Fractional KdV Equations Kuwait Journal of Science 41 (2014), 75-84.

H. A. Ghany and A. Hyder, Abundant solution of Wick-type stochastic fractional 2D KdV Equation Chin. Phys. B 23, No.6 (2014) 060503-7

H. A. Ghany and M. S. Mohammed, White noise functional solutions for the Wick-type stochastic fractional KdV-Burgers-Kuramoto equations Chin. J. Phys., 50 (2012), 619-627.

H. A. Ghany, A. S. Okb El Bab, A. M. Zabal and A. Hyder,The fractional coupled KdV equations:Exact solutions and white noise functional approach, Chin. Phys. B 22, (2013), 0805011-7.

J. H. He,A coupling method of homotopy technique and a perturbation technique for non-linear problems , Int. J. Non. Mech. 35 (2000),37-43.

J. H. He,Some asymptotic methods for strongly nonlinear equations , Int. J. Modern Phys. B, 20 (2006), 1141-1199.

J. H. He, Nonperturbative methods for strongly nonlinear problems, Dissertation, de-Verlag im Internet GmbH, 2006.

J. H. He and X. H. Wu,Construction of Solitary Solution and Compton-Like Solution by Variational Iteration Method, Chaos Solitons and Fractals, 29 (2006), 108-113.

[J .H. He and X. H. Wu, Exp-function method for nonlinear wave equations, Chaos Solitons and Fractals, 30 (2006), 700-708.

J. H. He and M. A. Abdou,New periodic solutions for nonlinear evolution equations using Exp-function method, Chaos Solitons and Fractals, 34 (2007), 1421-1429.

H. Holden, B. Osendal, J. Uboe and T. Zhang, Stochastic partial differential equations, Bihkäuser: Basel, 1996.

R. S. Johnson, A nonlinear equation incorporating damping and dispersion J. Fluid Mech.,42 (1970), 49-60.

H. M. Liu, A nonlinear equation incorporating damping and dispersion, Int. J. Non Sci. Numer. Simul., 5 (2004), 95-96.

J. Printems, The Stochastic Korteweg--de Vries Equation in L2, J. Differential Equations, 153 (1999), 338-373.

M. Wadati, Stochastic Korteweg-de Vries Equation, J. Phys. Soc. Jpn., 52 (1983), 2642-2648.

L. V. Wijngaarden, On the motion of gas bubbles in a perfect fluid, Annu. Rev. Fluid Mech., 4 (1972), 369-373.

X. H. Wu and J.H. He, EXP-function method and its application to nonlinear equations, Chaos Solitons and Fractals, 38 (2008), 903-910.

Y. C. Xie, Exact solutions for stochastic KdV equations , Phys. Lett. A, 310 (2003) 161-167.

Y.N. Zayko, Polarization waves in nonlinear dielectric, Zh. Teck. Fiz., 59 (1989), 172-173.

Y. N. Zayko and I. S. Nefedov, New class of solutions of the Kortewegde VriesBurgers equation, Appl. Math. Lett., 14 (2001), 115-121.

S. Zhang, Application of Exp-function method to high-dimensional nonlinear evolution equation, Chaos Solitons and Fractals, 38 (2008), 270-276.

S. D. Zhu, Exp-function Method for the Hybrid-Lattice System, Int J Non Sci Numer Simul 8 (2007), 461-464.

S. D. Zhu, Exp-function Method for the Discrete mKdV Lattice, Int J Non Sci Numer Simul, 8 (2007), 465-468.

### Refbacks

- There are currently no refbacks.

Please send any question about this web site to info@praiseworthyprize.com**Copyright © 2005-2024**** Praise Worthy Prize**