Numerical solution for a general class of nonlocal nonlinear wave equations arising in elasticity

Gulcin M. Muslu; Handan Borluk

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Numerical solution for a general class of nonlocal nonlinear wave equations arising in elasticity

机译：弹性中产生的一般非局部非线性波方程的数值解

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A class of nonlocal nonlinear wave equation arises from the modeling of a one dimensional motion in a nonlinearly, nonlocally elastic medium. The equation involves a kernel function with nonnegative Fourier transform. We discretize the equation by using Fourier spectral method in space and we prove the convergence of the semidiscrete scheme. We then use a fully-discrete scheme, that couples Fourier pseudo-spectral method in space and 4th order Runge-Kutta in time, to observe the effect of the kernel function on solutions. To generate solitary wave solutions numerically, we use the Petviashvili's iteration method.

机译：从非线性非局部弹性介质中的一维运动的建模中出现了一类非局部非线性波动方程。该等方程涉及具有非负傅里叶变换的内核函数。我们通过在空间中使用傅立叶光谱法使等式离散化，我们证明了半同函数方案的收敛性。然后，我们使用完全离散的方案，将傅立叶伪光谱法在空间和第四阶runge-Kutta上耦合，以观察内核功能对解决方案的影响。为了数控产生孤立波解决方案，我们使用PETVIASHVILI的迭代方法。

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来源
《Zeitschrift fur Angewandte Mathematik und Mechanik》 |2017年第12期|共11页
作者
Gulcin M. Muslu; Handan Borluk;
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作者单位

Istanbul Technical University Department of Mathematics Maslak 34469 Istanbul Turkey;

Istanbul Kemerburgaz University Department of Basic Sciences Bagcilar 34217 Istanbul Turkey;

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原文格式 PDF
正文语种 eng
中图分类应用数学;力学;
关键词
Nonlocal nonlinear wave equation; Boussinesq equations; Fourier pseudo-spectral method; Semi-discrete scheme; Convergence; Petviashvili's iteration method.;

机译：非局部非线性波方程;Boussinesq方程;傅立叶伪光谱法;半离散方案;收敛;Petviashvili的迭代方法。;

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专利

1. Numerical solution for a general class of nonlocal nonlinear wave equations arising in elasticity [J] . Gulcin M. Muslu, Handan Borluk Zeitschrift fur Angewandte Mathematik und Mechanik . 2017,第12期

机译：弹性中产生的一般非局部非线性波方程的数值解
2. Haar wavelet based numerical solution of nonlinear differential equations arising in fluid dynamics [J] . S. C. Shiralashetti, M. H. Kantli, A. B. Deshi International Journal of Computational Materials Science and Engineering . 2016,第2期

机译：基于Haar小波的流体动力学非线性微分方程数值解。
3. Numerical solution of some nonlocal, nonlinear dispersive wave equations [J] . Pelloni B., Dougalis VA. Journal of nonlinear science . 2000,第1期

机译：一些非局部非线性色散波方程的数值解
4. On the Nonlocal Symmetries, Group Invariant Solutions and Conservation Laws of the Equations of Nonlinear Dynamical Compressible Elasticity [C] . G. W. Bluman, A. R. Cheviakov, J. F. Ganghoffer IUTAM Symposium on Progress in the Theory and Numerics of Configurational Mechanics . 2009

机译：在非局部对称，组不变解和非线性动力学可压缩弹性方程的局部解决方案和保护规律
5. Numerical solutions of the Hamilton-Jacobi equations arising in nonlinear H(infinity) and optimal control. [D] . Markman, Jerry. 1998

机译：非线性H（无穷大）中的Hamilton-Jacobi方程的数值解和最优控制。
6. Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation [O] . Wei Liu, Jing Zhang, Xiliang Li 2012

机译：二维非局部非线性Schrödinger方程和非局部Klein-Gordon方程中的无赖波
7. Numerical Solution Of Some Nonlocal, Nonlinear Dispersive Wave Equations [O] . Beatrice Pelloni, Vassilios A. Dougalis 1999

机译：一些非局部非线性色散波方程的数值解
8. Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves [R] . Eringen, A. C. 1983

机译：非局部弹性微分方程及螺旋位错和表面波的解

Numerical solution for a general class of nonlocal nonlinear wave equations arising in elasticity

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