Analysis of the Solutions of the Equation Modeled in the Field of Nonlinear Sciences
Yıl 2020,
Cilt: 10 Sayı: 3, 2009 - 2020, 01.09.2020
Tolga Aktürk
,
Mahşure Kübranur Dikici
Öz
In this article, the travelling wave solutions of the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur (AKNS) equation are investigated using the modified exponential function method (MEFM). This method is used to find analytical travelling wave solutions of the AKNS equation. The different travelling wave solutions are obtained by determining the appropriate values for the parameters. Two and three dimensional graphics of the different wave solutions found in this way are plotted with the help of Mathematica package program by determining the appropriate parameters.
Kaynakça
- Baskonus HM, Bulut H, 2016. Exponential prototype structures for (2+1)-dimensional Boiti-Leon-Pempinelli systems in mathematical physics. Waves in Random and Complex Media, 26(2): 189-196.
- Bruzón MS, Gandarias ML, Muriel C, Ramirez J, Romero FR, 2003. Traveling-Wave Solutions of the Schwarz–Korteweg–de Vries Equation in 2+ 1 Dimensions and the Ablowitz–Kaup–Newell–Segur Equation Through Symmetry Reductions. Theoretical and mathematical physics, 137(1): 1378-1389.
- Bulut H, Akturk T, Gurefe Y, 2015. An application of the new function method to the generalized double sinh-Gordon equation. AIP Conference Proceedings, 1648(1): 4 pp.
- Bulut H, Atas SS, Baskonus HM, 2016. Some novel exponential function structures to the Cahn–Allen equation. Cogent Physics, 3(1);1240886.
- Bulut H, Yel G, Başkonuş HM, 2016. An application of improved Bernoulli sub-equation function methodto the nonlinear time-fractional burgers equation. Turkish Journal of Mathematics and ComputerScience, 5: 1-7.
- Helal MA, Seadawy AR, Zekry MH, 2013. Stability analysis solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave equation. Applied Mathematical Sciences, 7(65-68): 3355-3365.
- Hirota R, 1973. Exact envelope‐soliton solutions of a nonlinear wave equation. Journal of Mathematical Physics 14(7): 805-809.
- Liu S, Fu Z, Liu S, Zhao Q, 2001. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Physics Letters A 289(1-2): 69-74.
- Naher H, Abdullah FA, 2013. New approach of (G′/G)-expansion method and new approach of generalized (G′/G)-expansion method for nonlinear evolution equation. American Inst. of Physics Advances, 3(3): 032116.
- Shen G, Sun Y, Xiong Y, 2013. New travelling-wave solutions for Dodd-Bullough equation, J. Appl. Math.2013: 5 pp.
- Sun Y, 2014. New travelling wave solutions for Sine-Gordon equation, J. Appl. Math. 2014: 4 pp.
- Yusufoğlu E, Bekir A, Alp M, 2008. Periodic and solitary wave solutions of Kawahara and modifiedKawahara equations by using Sine–Cosine method. Chaos, Solitons & Fractals, 37(4): 1193-1197.
- Zhang JL, Wang ML, Li XZ, 2006. The subsidiary ordinary differential equations and the exact solutionsof the higher order dispersive nonlinear Schrödinger equation. Physics Letters A 357(3): 188-195.
- Zheng B, 2011. A new Bernoulli sub-ODE method for constructing traveling wave solutions for two nonlinear equations with any order. University Politechnica of Bucharest Scientific Bulletin Series A, 73(3): 85-94.
- Zhou Y, Wang M, Miao T, 2004. The periodic wave solutions and solitary wave solutions for a class of nonlinear partial differential equations. Physics Letters A 323(1-2): 77-88.
- Wang M, Li X, Zhang, J, 2008. The (G′/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Physics Letters A 372(4): 417-423.
Analysis of the Solutions of the Equation Modeled in the Field of Nonlinear Sciences
Yıl 2020,
Cilt: 10 Sayı: 3, 2009 - 2020, 01.09.2020
Tolga Aktürk
,
Mahşure Kübranur Dikici
Öz
In this article, the travelling wave solutions of the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur (AKNS) equation are investigated using the modified exponential function method (MEFM). This method is used to find analytical travelling wave solutions of the AKNS equation. The different travelling wave solutions are obtained by determining the appropriate values for the parameters. Two and three dimensional graphics of the different wave solutions found in this way are plotted with the help of Mathematica package program by determining the appropriate parameters.
Kaynakça
- Baskonus HM, Bulut H, 2016. Exponential prototype structures for (2+1)-dimensional Boiti-Leon-Pempinelli systems in mathematical physics. Waves in Random and Complex Media, 26(2): 189-196.
- Bruzón MS, Gandarias ML, Muriel C, Ramirez J, Romero FR, 2003. Traveling-Wave Solutions of the Schwarz–Korteweg–de Vries Equation in 2+ 1 Dimensions and the Ablowitz–Kaup–Newell–Segur Equation Through Symmetry Reductions. Theoretical and mathematical physics, 137(1): 1378-1389.
- Bulut H, Akturk T, Gurefe Y, 2015. An application of the new function method to the generalized double sinh-Gordon equation. AIP Conference Proceedings, 1648(1): 4 pp.
- Bulut H, Atas SS, Baskonus HM, 2016. Some novel exponential function structures to the Cahn–Allen equation. Cogent Physics, 3(1);1240886.
- Bulut H, Yel G, Başkonuş HM, 2016. An application of improved Bernoulli sub-equation function methodto the nonlinear time-fractional burgers equation. Turkish Journal of Mathematics and ComputerScience, 5: 1-7.
- Helal MA, Seadawy AR, Zekry MH, 2013. Stability analysis solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave equation. Applied Mathematical Sciences, 7(65-68): 3355-3365.
- Hirota R, 1973. Exact envelope‐soliton solutions of a nonlinear wave equation. Journal of Mathematical Physics 14(7): 805-809.
- Liu S, Fu Z, Liu S, Zhao Q, 2001. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Physics Letters A 289(1-2): 69-74.
- Naher H, Abdullah FA, 2013. New approach of (G′/G)-expansion method and new approach of generalized (G′/G)-expansion method for nonlinear evolution equation. American Inst. of Physics Advances, 3(3): 032116.
- Shen G, Sun Y, Xiong Y, 2013. New travelling-wave solutions for Dodd-Bullough equation, J. Appl. Math.2013: 5 pp.
- Sun Y, 2014. New travelling wave solutions for Sine-Gordon equation, J. Appl. Math. 2014: 4 pp.
- Yusufoğlu E, Bekir A, Alp M, 2008. Periodic and solitary wave solutions of Kawahara and modifiedKawahara equations by using Sine–Cosine method. Chaos, Solitons & Fractals, 37(4): 1193-1197.
- Zhang JL, Wang ML, Li XZ, 2006. The subsidiary ordinary differential equations and the exact solutionsof the higher order dispersive nonlinear Schrödinger equation. Physics Letters A 357(3): 188-195.
- Zheng B, 2011. A new Bernoulli sub-ODE method for constructing traveling wave solutions for two nonlinear equations with any order. University Politechnica of Bucharest Scientific Bulletin Series A, 73(3): 85-94.
- Zhou Y, Wang M, Miao T, 2004. The periodic wave solutions and solitary wave solutions for a class of nonlinear partial differential equations. Physics Letters A 323(1-2): 77-88.
- Wang M, Li X, Zhang, J, 2008. The (G′/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Physics Letters A 372(4): 417-423.