Solitary wave solution of nonlinear multi-dimensional wave equation by bilinear transformation method |
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| Institution: | 1. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762, USA;2. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;3. Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan;1. Department of Physics, University of the Western Cape, Bellville 7535, South-Africa;2. Office of the Deputy Vice Chancellor (Academic), University of the Western Cape, Bellville, South-Africa;3. Indian Institute of Geomagnetism, New Panvel (W), Navi Mumbai, India;1. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China;2. Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA;3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, China;4. College of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China;5. International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa;1. Department of Mathematics, West Bengal State University, Barasat, Kolkata 700126, India;2. Plasma Physics Group, Theoretical Physics Laboratory, Faculty of Sciences-Physics, University of Bab-Ezzouar, U.S.T.H.B B.P. 32, El Alia, Algiers 16111, Algeria;1. Theoretical Physics Group, Physics Department, Faculty of Science, Hail University, Saudi Arabia;2. Department of Physics, Taibah University, Al-Madinah Al-Munawarrah, Saudi Arabia;3. College of Science and Humanitarian Studies, Physics Department, Prince Sattam Bin Abdul Aziz University, Saudi Arabia;4. Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt |
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| Abstract: | The Hirota method is applied to construct exact analytical solitary wave solutions of the system of multi-dimensional nonlinear wave equation for n-component vector with modified background. The nonlinear part is the third-order polynomial, determined by three distinct constant vectors. These solutions have not previously been obtained by any analytic technique. The bilinear representation is derived by extracting one of the vector roots (unstable in general). This allows to reduce the cubic nonlinearity to a quadratic one. The transition between other two stable roots gives us a vector shock solitary wave solution. In our approach, the velocity of solitary wave is fixed by truncating the Hirota perturbation expansion and it is found in terms of all three roots. Simulations of solutions for the one component and one-dimensional case are also illustrated. |
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