含气泡液体中三维非线性波方程
Equation for three-dimensional nonlinear waves in liquid with gas bubbles
摘要：
在三维情况下，考虑了含气泡液体中的非线性波。给出了描述长非线性压力波的非线性发展方程。结果表明，在一般情况下，方程是不可积的。给出了非线性发展方程的一些精确解。应用广田方法求解三维不可积演化方程的多孤子解。研究了一维孤立波的稳定性。结果表明，一维孤立波对横向扰动是稳定的。
英文摘要：
Nonlinear waves in a liquid containing gas bubbles are considered in the three-dimensional case. Nonlinear evolution equation is given for description of long nonlinear pressure waves. It is shown that in the general case the equation is not integrable. Some exact solutions for the nonlinear evolution equation are presented. Application of the Hirota method is illustrated for finding multi-soliton solutions for the nonintegrable evolution equation in the three-dimensional case. The stability of the one-dimensional solitary waves is investigated. It is shown that the one-dimensional solitary waves are stable to transverse perturbations.
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