标题： 四阶模顿在旋转自引力流体中 显示英文标题

标题： Fourth-order modon in a rotating self-gravitating fluid

摘要： 我们提出一个二维非线性方程来描述旋转自引力流体中扰动的动力学。 该方程的非线性项具有泊松括号（雅可比）的形式，线性部分除了拉普拉斯算子外，还包括双调和算子。 找到了一个偶极涡旋（模顿）形式的解。 该解及其到四阶的所有导数在分离子上都是连续的。 显示英文摘要

摘要： We present a two-dimensional nonlinear equation to govern the dynamics of disturbances in a rotating self-gravitating fluid. The nonlinear term of the equation has the form of a Poisson bracket (Jacobian), and the linear part contains, along with the Laplacian, a biharmonic operator. A solution was found in the form of a dipole vortex (modon). The solution and all its derivatives up to the fourth order are continuous on the separatrix.