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Complex acoustic gravity wave behaviors to some mathematical models arising in fluid dynamics and nonlinear dispersive media

机译:流体动力学和非线性弥散介质中某些数学模型的复声重力波行为

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摘要

This study acquires the wave solutions of the two well-known nonlinear models, namely; the modified Benjamin-Bona-Mahony and the coupled Klein-Gordon equations. The modified Benjamin-Bona-Mahony is a nonlinear model that describes the long surface gravity waves of small amplitude and the coupled Klein-Gordon equation describes the quantized version of the relativistic energy-momentum relation. We successfully acquire some new solutions to these models such as kink-type and soliton solutions in complex hyperbolic functions form. We plot the 3D and 2D surface of the all the obtained solutions in this study. The mathematical approach used in this study is the sine-Gordon expansion method.
机译:本研究获得了两个著名的非线性模型的波动解。修改后的本杰明·博纳·马奥尼方程和耦合的克莱因·戈登方程。修改后的本杰明-波纳-马洪尼是一个非线性模型,描述了小振幅的长表面重力波,耦合的克莱因-戈登方程描述了相对论能量动量关系的量化形式。我们成功地获得了这些模型的一些新解,例如复杂双曲函数形式的扭结型和孤子解。在这项研究中,我们绘制了所有获得的解决方案的3D和2D表面。本研究中使用的数学方法是正弦-戈登展开法。

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