New Exact Solutions of (3+1)-dimensional Kadomtsev-Petviashvili (KP) Equation

Yıl 2020, , 120 - 125, 23.10.2020

Yusuf Pandır , Tural Ağır

https://doi.org/10.46810/tdfd.731464

Öz

The extended trial equation method is investigated which allows us to achieve soliton solutions and Jacobi elliptic function solution of the partial differential equations. This method is implemented to the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation and various new exact solutions have been obtained. These new obtain exact solutions are solutions that are not known in the literature. Additionally, two and three-dimensional graphics were drawn to understand the physical behaviors of the distinct obtain exact solutions.

Anahtar Kelimeler

Extended Trial Equation Method, (3+1) Dimensional Kadomtsev-Petviashvili (KP) Equation, Exact Solutions

(3 + 1) boyutlu Kadomtsev-Petviashvili (KP) Denkleminin Yeni Tam Çözümleri

Öz

Kısmi türevli diferansiyel denklemlerin soliton çözeltilerini ve Jacobi eliptik fonksiyon çözümlerini elde etmemizi sağlayan genişletilmiş deneme denklemi yöntemi araştırılmıştır. Bu yöntem (3+1)-boyutlu Kadomtsev-Petviashvili (KP) denklemine uygulanmış ve çeşitli yeni tam(kesin) çözümler elde edilmiştir. Bu yeni tam çözümler, literatürde yer almayan çözümlerdir. Ek olarak, elde edilen farklı tam çözümlerin fiziksel davranışlarını anlamak için iki ve üç boyutlu grafikler çizilmiştir.

Anahtar Kelimeler

Genişletilmiş deneme denklemi yöntemi, (3+1)-boyutlu Kadomtsev-Petviashvili (KP) denklemi, tam çözümler

Kaynakça

• Wazwaz AM. A sine-cosine method for handling nonlinear wave equations. Mathematical and Computer Modeling 2008; 40(5-6): 499-08. doi:10.1016/j.mcm.2003.12.010
• Wang ML. Exact solutions for compound KdV-Burgers equations. Physics Letters A 1996; 213:279-87. doi:10.1016/0375-9601(96)00103-X
• Hietarinta J. Hirota's bilinear method and its generalization. International Journal of Modern Physics A 1997; 12(1): 43-1. doi:10.1142/S0217751X97000062
• Pashaev O, Tanoglu G. Vector shock soliton and the Hirota bilinear method. Chaos, Solitons & Fractals 2005; 26: 95-105. doi.org/10.1016/j.chaos.2004.12.021
• Akbar MA, Ali NHM, Mohyud-Din ST. The modified alternative G'/G -expansion method to nonlinear evolution equation: application to the (1+1)-dimensional Drinfel’d-Sokolov-Wilson equation. SpringerPlus 2013; 327: 2-16. doi:10.1186/2193-1801-2-327
• Shakeel M, Mohyud-Din ST. New G'/G -expansion method and its application to the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK–BBM) equation. Journal of the Association of Arab Universities for Basic & Applied Science 2015; 18(1): 66-81. doi:10.1016/j.jaubas.2014.02.007
• Liu CS. Trial equation method for nonlinear evolution equations with rank inhomogeneous: mathematical discussions and applications. Communications in Theoretical Physics 2006; 45(2): 219-23. doi:10.1088/0253-6102/45/2/005
• Liu CS. Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations. Computer Physics Communications 2010; 181(2): 317-24. doi:10.1016/j.cpc.2009.10.006
• Gurefe Y, Sonmezoglu A, Misirli E. Application of trial equation method to the nonlinear partial differential equations arising in mathematical physics. Pramana-Journal of Physics 2011; 77(6): 1023-9. doi: 10.1007/s12043-011-0201-5
• Gurefe Y, Sonmezoglu A, Misirli E. 2012. Application of an irrational trial equation method to high dimensional nonlinear evolution equations. Journal of Advanced Mathematical Studies 2012; 5(1): 41-7.
• Pandir Y, Gurefe Y, Kadak U, Misirli E. Classifications of exact solutions for some nonlinear partial differential equations with generalized evolution. Abstract and Applied Analysis 2012; 2012: 1-16. doi:10.1155/2012/478531
• Pandir Y, Gurefe Y, Misirli E. Classification of exact solutions to the generalized Kadomtsev-Petviashvili equation. Physica Scripta 2013; 87(2):1-12. doi:10.1088/0031-8949/87/02/025003
• Gurefe Y, Misirli E, Sonmezoglu A, Ekici M. Extended trial equation method to generalized nonlinear partial differential equations. Applied Mathematics and Computation 2013; 219(10): 5253-60. doi:10.1016/j.amc.2012.11.046
• Pandir Y. Symmetric Fibonacci function solutions of some nonlinear partial differential equations. Applied Mathematics & Information Science 2014; 8: 2237-41. doi:10.12785/amis/080518
• Tandogan YA, Pandir Y, Gurefe Y. Solutions of the nonlinear differential equations by use of modified Kudryashov method. Turkish Journal of Mathematics and Computer Science 2013; 1: 54-60.
• Ma WX. Comment on the (3+1)-dimensional Kadomtsev-Petviashvili equations. Communications Nonlinear Science & Numerical Simulation 2011; 16(7): 2663-66. doi:10.1016/j.cnsns.2010.10.003
• Osman MS. Nonlinear interaction of solitary waves described by multi-rational wave solutions of the (2+1)-dimensional Kadomtsev-Petviashvili equation with variable coefficients. Nonlinear Dynamics 2017; 87(2): 1209-16. doi: 10.1007/s11071-016-3110-9
• Chen Y, Yan Z, Zhang H. New explicit solitary wave solutions for (2+1)-dimensional Boussinesq equation and (3+1)-dimensional KP equation. Physics Letters A 2003; 307: 107-13. doi:10.1016/S0375-9601(02)01668-7
• Lu D, Tariq KU, Osman MS, Baleanu D, Younis M, Khater MMA. New analytical wave structures for the (3+1)-dimensional Kadomtsev-Petviashvili and the generalized Boussinesq models and their applications. Results in Physics 2019; 14: 102491. doi.org/10.1016/j.rinp.2019.102491
• Ablowitz MJ, Clarkson PA. Solitons, nonlinear evolution equations and inverse scattering, Cambridge, Cambridge University Press; 1991.
• Wazwaz AM. Multiple-soliton solutions for the KP equation by Hirota’s bilinear method and by the tanh-coth method. Applied Mathematics and Computation 2007; 190(1): 633-40. doi.org/10.1016/j.amc.2007.01.056
• Sinelshchikov DI. Comment on: new exact traveling wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation. Communications Nonlinear Science & Numerical Simulation 2010; 15: 3235-36. doi:10.1016/j.cnsns.2009.11.028
• Khalfallah M. New exact traveling wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation. Communications Nonlinear Science & Numerical Simulation 2009; 14: 1169-75. doi.org/10.1016/j.cnsns.2007.11.010