Soliton solutions of coupled higgs field equation via the trial equation method

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    Since a few recent decades, investigation of nonlinear evolution equations (NLEEs) is becoming an important area of research as they have a variety of applications in various branches of social and scientific disciplines like Ecology, Social Dynamics, Financial Mathematics, Engineering and many branches of Physics such as Biophysics, Chemical Physics, Fibre Optics, Fluid Mechanics, Neuro-physics, Particle Physics, Solid State Physics and many more. Many powerful and efficient methods of finding exact solutions of NLEEs have been proposed so far and the Trial Equation Method [ 1 - 5] is one of them. Many authors have successfully used the method in finding exact solutions of a number of NLEEs. In the present paper, soliton solutions of the Coupled Higgs Field Equation [ 6 - 10 ] are being obtained using the Trial Equation Method.

     The Coupled Higgs Field Equation describes system of conserved scalar nucleons interacting with neutral scalar mesons in particle physics. This coupled equation has applications in the studies of Field Theory and Electromagnetic waves as well. This coupled equation introduces the Higgs field to illustrate the mechanism of generation of mass for Gauge Bosons. The Coupled Higgs Field Equation is generally expressed as the following pair of NLEEs

     

                                                                                                                                                             (3)

     

    and

     

                                                                                                                                                                             (2)

     

    Here, x and t are spatial and temporal variables respectively, the function  is a complex scalar nucleon field, the function  is a real scalar meson field,  are arbitrary real constants and the subscripts denote partial differentiations with respect to them.

    Using the Trial Equation Method, the above coupled NLEE is to be solved to obtain some soliton solutions.


  • Keywords


    .

  • References


      [1] LIU Cheng-Shi, Trial Equation Method to Nonlinear Evolution Equations with Rank Inhomogeneous: Mathematical Discussions and Its Applications, Commun. Theor. Phys. (Beijing, China), 2006, 45(2), 219–223. https://doi.org/10.1088/0253-6102/45/2/005.

      [2] Triki, Houria; Wazwaz, A. M., Trial equation method for solving the generalized Fisher equation with variable coefficients, Phys. Lett. A, 2016. https://doi.org/10.1016/j.physleta.2016.02.002.

      [3] Li, Yang, Application of Trial Equation Method for Solving the Benjamin Ono Equation, JAMP, 2014, 2, 45 – 49. https://doi.org/10.4236/jamp.2014.23005.

      [4] Biswas, A.; Yildrim, Y.; Yasar, E.; Triki, H.; Alshomrani, A. S.; Ullah, M. Z.; Zhou, Q.; Moshokoa, S. P.; Belic, M.; Optical soliton perturbation with full nonlinearity by trial equation method, Optik, 2018, 157, 1366 – 1375. https://doi.org/10.1016/j.ijleo.2017.12.113.

      [5] Biswas, A.; Yildrim,Y.; Yasar, E.; Zhou,Q.; Alshomrani, A. S.; Moshokoa, S. P.; Belic, M.; Dispersive optical solitons with Schrödinger–Hirota model by trial equation method, Optik, 2018, 162, 35 – 41. https://doi.org/10.1016/j.ijleo.2018.02.058.

      [6] Alquran, M.; Katatbeh, Q.; Al-Shrida, B.; Applications of First Integral Method to Some Complex Nonlinear Evolution Systems, Appl. Math. Inf. Sci., 2015, 9(2), 825-831.

      [7] Wazwaz, A. M.; Abundant soliton and periodic wave solutions for the coupled Higgs field equation, the Maccari system and the Hirota–Maccari system, Phys. Scr. 2012, 85, 065011 (10pp), stacks.iop.org/PhysScr/85/065011. https://doi.org/10.1088/0031-8949/85/06/065011.

      [8] Abdelkawy, M.A.; Bhrawy, A.H.; Zerrad,E.; Biswas, A.; Application of Tanh Method to Complex Coupled Nonlinear Evolution Equations, ‎Acta Phys. Pol. A, 2016, 129(3), 278 – 283. https://doi.org/10.12693/APhysPolA.129.278.

      [9] Jabbari A.; Kheiri, H.; Bekir, A.; Exact solutions of the coupled Higgs equation and the Maccari system using He’s semi-inverse method and -expansion method, Comput. Math. Appl., 2011, 62, 2177 – 2186. https://doi.org/10.1016/j.camwa.2011.07.003.

      [10] Khater, M. M. A.; Seadawy, A. R.; Lu, D.; Dispersive solitary wave solutions of new coupled Konno-Oono, Higgs field and Maccari equations and their applications, J. King Saud Univ. Sci., 2018, 30, 417 – 423. https://doi.org/10.1016/j.jksus.2017.11.003.


 

View

Download

Article ID: 29859
 
DOI: 10.14419/ijpr.v7i2.29859




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.