Traveling wave solutions of the nonlinear Gilson-Pickering equation in crystal lattice theory  

作　　者：A.T.Nguyen O.Nikan Z.Avazzadeh 

机构地区：[1]Division of Applied Mathematics,Science and Technology Advanced Institute,Van Lang University,Ho Chi Minh City,Vietnam [2]Faculty of Technology,Van Lang University,Ho Chi Minh City,Vietnam [3]School of Mathematics,Iran University of Science and Technology,Narmak,Tehran,Iran [4]Department of Applied Mathematics,Xi’an Jiaotong-Liverpool University,Suzhou 215123,China

出　　处：《Journal of Ocean Engineering and Science》2024年第1期40-49,共10页海洋工程与科学（英文）

摘　　要：This paper focuses on obtaining the traveling wave solutions of the nonlinear Gilson-Pickering equa-tion(GPE),which describes the prorogation of waves in crystal lattice theory and plasma physics.The solution of the GPE is approximated via the finite difference technique and the localized meshless radial basis function generated finite difference.The association of the technique results in a meshless approach that does not require linearizing the nonlinear terms.At the first step,the PDE is converted to a system of nonlinear ODEs with the help of the radial kernels.In the second step,a high-order ODE solver is adopted to discretize the nonlinear ODE system.The global collocation techniques pose a considerable computationl burden due to the calculation of the dense algebraic system.The proposed method approx-imates differential operators over the local support domain,leading to sparse differentiation matrices and decreasing the computational burden.Numerical results and comparisons are provided to confirm the efficiency and accuracy of the method.

关 键 词：Nonlinear Gilson–Pickering equation Soliton wave solutions Meshless technique RBF LRBF-FD Optimal shape parameter 

分 类 号：O17[理学—数学]