Solving (3+1) D- New Hirota Bilinear Equation Using Tanh Method and New Modification of Extended Tanh Method

Solving (3+1) D- New Hirota Bilinear Equation Using Tanh Method and New Modification of Extended Tanh Method

Authors

  • Zainab H. Kareem, Luma N. M. Tawfiq

Keywords:

Nonlinear PDEs; Hirote bilinear equation (HBE); Tanh method; Extended tanh method

Abstract

In this article Tanh method is considered as effective approach to get solutions of some types of non-linear partial differential equations. Then we suggested new modification for extended Tanh method as highly effective approach to obtaining precise traveling wave solutions to these types of equations. Then using both methods, to solve the (3+1) D- new Hirote bilinear equation (NHBE) and then we compare between the results to illustrate the effectiveness of suggested modification. The interpretation of these solutions presented graphical to illustrate behaviors of the solutions gives us some popular shapes include solutions of type solitary wave, the singular wave, the kink wave, and the singular kink wave.

References

H. Salih, Solving Modified Regularized Long Wave Equation using Collo cation Metho d. JPCS. Vol. 1003, No. 012062, pp: 1-10, 2018.

N.A. Hussein, L.N. M. Tawfiq, Efficien t Approac h for Solvin g High Ord er (2+1) D-Differen tial Equation, AIP Conference Pro ceedin gs, 2398, 10, pp: 1-11, 2022.

N.A., Hussein, New Approac h for Solving (1+1) -Dimensional Differen tial Equation. JPCS. Vol. 1530, No. 012098, pp. 1-11, 2020.

B .Guo, L .Ling, QP . Liu. Nonlinear Sc hr¨odinger equation: generalized Darb oux tra nsformation and rogue wave solutions. Ph ys Rev E. 2012; 85(2):026607.

Z. H. K areem, Recen t modification of decomp osition metho d for solving wave-like Equation, Journal of Interdisciplinary Mathematics, Vol. 26, No. 5, pp. 809–820, 2023

A.H. Khamas, New Approac h for Calculate Exp onential Integra l Function. Iraqi Journal of Science, 64(8), pp. 4034–4042, 2023.

L.N. M. Tawfiq, N.A. Hussein, Exact soliton solution for systems of non-linear (2+1)D-DEs, AIP Conf. Pro c., AIP Conf. Pro c. 2834, 080137, p.1-7, 2023.

Ali, MH, Tawfiq, LNM. Design Optimal Neural Net work for Solving Unsteady State Confined Aquifer Problem, Mathe- matical Modelling of Engineering Problems, 2023, 10, 2, 565-571.

A. H. Khamas, Determine the Effect Hookah Smoking on Health with Differen t Typ es of Tobacco by using P arallel Pro cessin g Technique, JPCS, 2021, 1818, 012175 : 1-10.

Kareem ZH, Efficien t Modification of the Dec omp osition Metho d for Solving a System of PDEs. Iraqi J . Sci. 2021; 62(9): 3061-3070.

N. A. Hussein, Double LA-transform and their prop erties for solvi ng partial differen tial equati ons, AIP Conf. Pro c., AIP Conf. P roc., 2834, 080140, p.1-10, 2023.

S.M. Yassien, Solution of High Order Ordinary Boundary Value Problems Using Semi-Analytic Technique, Ibn Al-Haitham Journal for Pure and Applied Sciences, 26, pp: 281-291, 2013.

J.H. He, Bo okkeeping parameter in perturbation metho ds, Int. J. Nonlin. Sci. Numer. Sim ul, 2 (20 01) 257–264.

M.T. Darvishi, A. Karami, B.-C. Shin , Application of He’s parameter expansion metho d for oscillat ors with smo oth odd nonlinearities, Ph ys. Lett. A, 372(33 ) (2008) 5381–5384.

B.-C. Shin, M.T. Darvishi, A. Karami, Application of He’s parameter expansion meth od to a nonlinear self-excited oscillator system, Int. J. Nonlin. Sci. Num. Sim ul., 10(1) (2009) 137–143.

M.T. Darvishi, S. Kheybari, A. Yildirim, Application of He’s parameter pxpansion metho d to a system of two van der P ol oscillators coupled via a bath, Nonlin. Science Lett. A., 1(4) (2010) 399–405.

FF. Ghazi, New Approac h for Solving Two Dimensional Spaces PDE. Journal of Ph ysics: Conference Series. 1530, 012066, pp: 1-10, 2020.

AQ. Ibrahim Ab ed, Efficien t Metho d for Solvin g Fourth Order PDEs, JPC 2021,1818, 012166 :1-10.

Salih H., Solution of Modified Equal Width Equation Using Quartic Trigonometric-Spline Metho d. J PCS . 1664, 012033: 1-10, 2020.

M.H. Ali, Efficien t Design of Neural Net works for Solving Third Order P artial Differen tial Equations, JPCS, vol. 1530, no. 1, p. 1-10, 2020.

S.J. Liao, A general approac h to get series solution of non-similarit y boundary-la yer flows, Comm un. Nonlin ear Sci. Numer. Sim ul., 14(5) (2009) 2144–2159 .

M.T. Darvishi, F . Khani, A series solution of the foam dra inag e equation, Compu t. Math. Appl., 58 (2009) 360–368. [23] AH. Khamas, New Coupled Metho d for Solving Burger’s Equation. J PCS . 1530: 1-11, 2020.121 Zainab H. Kareem and Luma N. M. Tawfiq, Adv. Theory Nonlinear Anal. Appl. 7 (2023), 114–122.

M.T. Darvishi, S. Kheybari and F. Khani, A nume rica l solution of the Kortew eg-de Vries equation by pseudosp ectral metho d using Darvishi’s preconditionings, Appl. Math. Comput., 182(1) 2006: 98–105.

M.T. Darvishi, M. Ja vidi, A numerical solution of Burgers’ equation by pseudosp ectral metho d and Darvishi’s precondi- tioning, Appl. Math. Comput., 173(1) (2006) 421–429.

M.T. Darvishi, F. Khani and S. Kheybari, Sp ectral collo cation solution of a generalized Hirota-Satsuma KdV equation, Int. J. Compu t. Math., 84(4) (2007) 541–551.

M.T. Darvishi, F. Khani, S. Kheybari, Sp ectral collo cation metho d and Darvishi’s precondi tionings to solv e the generalized Burgers-Huxley equation, Comm un., Nonlinear Sci. Numer. Sim ul., 13(10) (2008) 2091– 2103.

J.H. He, X.H. Wu, Construction of solitary solution and compacton-lik e solution by variational iteration metho d, Chaos, Solitons and Fractals, 29 (2006) 108–1 13.

F. Khani, S. Hamedi-Nezhad, M.T. Darvishi, S.-W. Ryu, New solitary wave and perio dic solutions of the foam drainage equation using the Expfunction metho d, Nonlin. Anal.: Real World Appl., 10 (2009) 1904–1911.

B.-C. Shin, M.T. Darvishi, A. Barati, Some exact and new solutions of the Nizhn ik-Novik ov-Vesselo v equation using the Exp-function metho d, Comput. Math. Appl. 58(11/12) (2009) 2147–2151.

X.H. Wu, J.H. He, Exp-function metho d and its application to nonlinear equations, Chaos, Solitons and Fra ctals, 38(3) (2008) 903–910.

J.H. He, X.H. Wu, Exp-function metho d for nonlinear wave equations, Chaos Solitons Fractals, 30(3 ) (2006) 700–708.

J.H. He, M.A. Ab dou, New perio dic solutions for nonlinear evolution equations using Exp-function metho d, Chaos Solitons Fractals, 34 (2007) 1421–1429.

G. A. Nursena, Y. Emrul lah, A new (3+1) dimensional Hirota bilinear equation: P ainla v´e integrabilit y, Lie symmetry analysis, and conserv ation laws, Journal of Taibah Univ ersit y for Science, VOL. 16, NO. 1, (2022) 1287–1297.

M. Zeynel and E. Yasar, A new (3 + 1) dimensional Hirota bilin ear equation: P erio dic, rogue, brigh t and dark wave solutions by bilinear neural net work metho d, Journal of Ocean Engineering and Science, m5G; May 2, 2022; 13:14.

M. Dong, S. Tian, X. Yan and L. Zou, Solitary waves, homo clinic breather waves and rogue waves of the (3 + 1)-dimensional Hirota bilinear equation, Computers and Mathematics with Applications, 75 (2018) 957-964.

W. Malfliet, Solitary wave solutions of nonlinear wave equations, Am. J. Ph ys. 60 (1992) 650–654.

A. M. Wazw az, Exact and explicit tra velling wave solutions for the nonlinear Drinfeld Sok olov syste m, Comm unicatio ns in nonlinear science and numerical simulation. 11 (3) (2006) 311–325.

N A Hussein, Solitary Wave Solu tion of Zakharo v-Kuznetso v Equation, AIP Conference Pro ceedings, Vol. 2398, Issue. 1, pp: 1-6, 2022.

A. M. Wazw az, Th e tanh metho d for compact and non compact solutions for varian ts of the KdV–Burger equations, Ph ys. D: Nonlinear Phenomena 213 (2) (2006) 147–151.

Downloads

Published

2023-12-30

How to Cite

Solving (3+1) D- New Hirota Bilinear Equation Using Tanh Method and New Modification of Extended Tanh Method. (2023). Advances in the Theory of Nonlinear Analysis and Its Application, 7(4), 114-122. https://doi.org/10.17762/atnaa.v7.i4.287