The new solitary solutions of the foam drainage & (2+1) dimensional breaking soliton equations

• Authors

• Emad H. M. Zahran faculty of science , zagazig University
• Maha S. M. Shehat faculty of engineering,Shubra,Benha university
2018-06-27
• Foam Drainage Equation, the (2 1)-Dimensional Breaking Soliton Equation, the Modified Extended Tanh-Function Method, Ricatti Equation, Travelling Wave Solution
• In this study, the modified extended tanh-function method is handling to obtain many new solitary wave solutions of two important models in nonlinear physics. The first one is the foam drainage equation which is a simple model for describing the flow of liquid through channels and nodes between the bubbles, driven by gravity and capillarity. The second is (2+1)-dimensional breaking soliton equation which describe the interaction of a Riemann wave propagating along the y-axis with along the x-axis. The obtained results are compared with that obtained in previous work.

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• References

1. [1] Younis, Muhammad. A new approach for the exact solutions of nonlinear equations offractional order via modified simple equation method. Applied Mathematics 5.13 (2014):1927.

[2] Emad H.M. Zahran., Mostafa M. A. Khater. The modified simple equation methodand its applications for solving some nonlinear evolutions equations in mathematicalphysics.Jokull journal 64.5 (2014): 297-312.

[3] Wang, Mingliang, Xiangzheng Li, and Jinliang Zhang.The (Gâ€² /G) -expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Letters A 372.4 (2008): 417-423.

[4] Ahmet Bekir, Ferat Uygun, Exact travelling wave solutions of some nonlinear evolution equations by using (Gâ€² /G)-expansion method.Arab Journal of Mathematical Sciences18 (2012) 73-85.

[5] Zhang, Sheng, Jing-Lin Tong, and Wei Wang. A generalized expansion method for the mKdV equation with variable coefficients, Physics Letters a, 37213 (2008): 2254-2257.

[6] Fan Engui and Jian Zhang. Applications of the Jacobi elliptic function method to special type nonlinear equations. Physics Letters a 305.6 (2002): 383-392.

[7] Emad H.M. Zahran. , Mostafa M. A. Khater. Exact Travelling wave solutions for the system of shallow water wave Equation Modified Liouvill Equation using Extended Jacobi Elliptic function Expansion Method. American Journal of computational Mathematics, 4 455-463. (December 2014).

[8] Maha S. M. Shehata, Extended Jacobi Elliptic function Expansion Method and its Applications for solving some Nonlinear Evolution Equations in Mathematical Physics. International Journal of Computer Applications, Vol.109-No.12. Jan. 2015.

[9] Emad H. M. Zahran. Exact traveling wave solutions for Nano-solitons of Ionic waves propagation along Microtubules in living cells and Nano-Ionic currents of MTs, World journal of Nano science and engineering,5,78-87,2015.

[10] Emad H. M. Zahran .Exact traveling wave solutions for Nano- Ionic solitons and Nano-Ionic currents of MTs using exp (âˆ’Ï† (Î¾))-expansion method, Advances in Nano particles, 4,25-36, 2015.

[11] Emad H. M. Zahran, Exact traveling wave solutions for nonlinear fractional partial differential equations arising in soliton using the exp (âˆ’Ï† (Î¾))-expansion method. International journal of computer applications. Vol.109, N.13, Jan. 2015.

[12] Maha S. M. Shehata, The exp (âˆ’Ï† (Î¾))- Method and Its Applications for Solving some Nonlinear Evolution Equations in Mathematical Physics , American Journal of ComputationalMathematics,2015,5,468-480.

[13] Emad H. M. Zahran , Travelling wave solutions of Non Linear Evolution Equation Via Modified exp (âˆ’Ï† (Î¾))-Expansion method, Journal of Computational and Theoretical Nanoscience,Vol.12,5716-5724, (2016).

[14] Yang, Xiao-Feng, Zi-Chen Deng, and Yi Wei. A Riccati-Bernoulli sub-ODE method fornonlinear partial differential equations and its application. Advances in Difference Equations.11 17, (2015).

[15] Maha S. M. Shehata, Anew solitary wave solution of the perturbed nonlinear Schrodinger equation using a Riccati Bernoulli Sub-ODE Method , International Journal of Physical Sciences, Vol.11 (6) pp.80-84, March.2016.

[16] Bekir, Ahmet, and Ahmet Boz. Exact solutions for a class of nonlinear partial differential Equations using exp-function method. International Journal of Nonlinear Sciences and Numerical Simulation 8.4 (2007): 505-512.

[17] Fan, Engui Extended tanh-function method and its applications to nonlinear equations. Physics Letters. A. 277.4(2000): 212-218.

[18] Maha S. M. Shehata. Exact Traveling Wave Solutions for Nonlinear Evolutions Equation Journal of Computational and Theoretical Nano science (2016) Vol.13.No.1, pp.534-538.2016.

[19] Elwakil, S. A., et al. Modified extended tanh-function method for

solving nonlinear partial differential equations. Physics Letters A

299.2(2002): 179-188.

[20] Emad H.M Zahran, and Mostafa M. A. Khatter,New solitary wave

solution of the generalized Hirota-Satsuma couple KdV system,

International Journal of scientific& Engineering Research,Vol

6,Isssue 8,August-2015Wang, G. W.

[21] Emad H.M Zahran, and Mostafa M. A. Khater. Modified extended

tanh-function method and its applications to the Bogoyavlenskii

equation. Applied Mathematical Modeling 40.3 (2016): 1769-1775.

[22] Emad H.M Zahran,Dianchin Lu and Mostafa M. A. Khater.Solitary

wave solution of the Benjamin-Bona-Mahoney-Burgers Equation

with Dual Power-Law Nonlinearity, Appl. Math.,Inf. Sci.,11,No.5,1-

5(2017)

[23] S. D. Stoyanov, V. N. Paunov, E.S. Basheva, I. B. Ivanov, A.

Mehreteab, G. Broze, Motion of the front between thick and thin film:

Hydrodynamic theory and experiment with vertical foam films,

Langmuir B (1997) 1400.

[24] R. Hirta, Y .Ohta, Hierarchies of coupled soliton equations I,J

phys.Sos.Jpn.60.(1991) 798.

[25] S.Zhang, New exact non-traveling wave and coefficient function

solutions of the (2+1) dimensional breaking soliton equations, Phys.

Lett. A. 368(2007) 470.

[26] Y.Cheng,B.Li, Symbolic computation and construction of soliton-

like solutions of the (2+1) dimensional breaking soliton equation,

Commun. Theor. Phys.(Beijing, China) 40 (2003) 137.

[27] Y. Z. Peng, New exact solutions for the (2+1) - dimensional break

ing soliton equation. Commun. Theor. Phys.(Beijing, China) 43

(2005) 205.

[28] Y. Z. Peng, E. V. Krishna, Two classes of new exact solutions to

the (2+1) dimensional breaking soliton equation, Commun. Theor.

Phys.(Beijing, China) 44 (2005) 807.