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The generalized fractional Benjamin–Bona–Mahony equation: Analytical and numerical results
Physica D: Nonlinear Phenomena ( IF 4 ) Pub Date : 2020-04-21 , DOI: 10.1016/j.physd.2020.132499
Goksu Oruc , Handan Borluk , Gulcin M. Muslu

The generalized fractional Benjamin–Bona–Mahony (gfBBM) equation models the propagation of small amplitude long unidirectional waves in a nonlocally and nonlinearly elastic medium. The equation involves two fractional terms unlike the well-known fBBM equation. In this paper, we prove local existence and uniqueness of the solutions for the Cauchy problem by using energy method. The sufficient conditions for the existence of solitary wave solutions are obtained. The Petviashvili method is proposed for the generation of the solitary wave solutions and their evolution in time is investigated numerically by Fourier spectral method. The efficiency of the numerical methods is tested and the relation between nonlinearity and fractional dispersion is observed by various numerical experiments.



中文翻译:

广义分数阶本杰明-波纳-马洪尼方程:解析和数值结果

广义分数阶本杰明-波纳-马洪尼(gfBBM)方程可模拟小振幅长单向波在非局部和非线性弹性介质中的传播。该方程涉及两个分数项,这与众所周知的fBBM方程不同。在本文中,我们使用能量方法证明了柯西问题的解的局部存在性和唯一性。获得了存在孤立波解的充分条件。提出了Petviashvili方法来生成孤立波解,并通过傅立叶谱方法对它们的时间演化进行了数值研究。测试了数值方法的效率,并通过各种数值实验观察了非线性与分数弥散之间的关系。

更新日期:2020-04-21
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