论文标题
在完整的分散kadomtsev-petviashvili方程中，用于分散弹性波
On the full dispersion Kadomtsev-Petviashvili equations for dispersive elastic waves
论文作者
论文摘要
从物理和数学的角度来看，水波的完整分散模型，例如Whitham方程和完整的分散kadomtsev-petviashvili（KP）方程都很有趣。本文研究了在非局部弹性培养基中传播的非线性弹性波的类似的完全色散模型。特别是我们考虑的抗平面剪切弹性波被认为是小振幅长波。在立方非线性和“负分散体”的情况下，我们提出了KP方程的两种不同的完全分散扩展。其中一个称为Whitham型全分散kp方程，另一个称为BBM型完全分散KP方程。文献中大多数现有的KP型方程是我们完整分散KP方程的特殊情况。我们还通过近似方程中的操作员来介绍新提出的完整分散KP方程的简化模型。我们表明，如果线孤立波的传播速度大于某个值，那么WHITHAM型完整分散kp方程的简化形式的线孤波解对长波长的横向干扰是线性不稳定的。对BBM型的完全分散KP方程的简化形式的类似分析不能提供线性不稳定性评估。
Full dispersive models of water waves, such as the Whitham equation and the full dispersion Kadomtsev-Petviashvili (KP) equation, are interesting from both the physical and mathematical points of view. This paper studies analogous full dispersive KP models of nonlinear elastic waves propagating in a nonlocal elastic medium. In particular we consider anti-plane shear elastic waves which are assumed to be small-amplitude long waves. We propose two different full dispersive extensions of the KP equation in the case of cubic nonlinearity and "negative dispersion". One of them is called the Whitham-type full dispersion KP equation and the other one is called the BBM-type full dispersion KP equation. Most of the existing KP-type equations in the literature are particular cases of our full dispersion KP equations. We also introduce the simplified models of the new proposed full dispersion KP equations by approximating the operators in the equations. We show that the line solitary wave solution of a simplified form of the Whitham-type full dispersion KP equation is linearly unstable to long-wavelength transverse disturbances if the propagation speed of the line solitary wave is greater than a certain value. A similar analysis for a simplified form of the BBM-type full dispersion KP equation does not provide a linear instability assessment.
