液体表面上的图案：椭圆余弦波，牛顿和缩放
Patterns on liquid surfaces: cnoidal waves, compactons and scaling
摘要：
研究了理想不可压缩液体在有界自由表面上的局部斑图和非线性振动的形成。本文讨论了椭圆余弦模、孤子和孤子作为非轴对称形状的传播。本文用有限差分微分广义Korteweg-de Vries方程来描述流体表面的三维运动和长浅通道的极限，重新得到著名的KdV方程。本文在图代数的基础上，对给定的初始条件，给出了一个非线性方程通解表示的试探性展开式。该模型是有用的多层流体动力学，团簇形成，和核物理，因为在整体规模，这些系统显示液体自由表面的行为。
英文摘要：
Localized patterns and nonlinear oscillation formation on the bounded free surface of an ideal incompressible liquid are analytically investigated . Cnoidal modes, solitons and compactons, as traveling non-axially symmetric shapes are discused. A finite-difference differential generalized Korteweg-de Vries equation is shown to describe the three-dimensional motion of the fluid surface and the limit of long and shallow channels one reobtains the well known KdV equation. A tentative expansion formula for the representation of the general solution of a nonlinear equation, for given initial condition is introduced on a graphical-algebraic basis. The model is useful in multilayer fluid dynamics, cluster formation, and nuclear physics since, up to an overall scale, these systems display liquid free surface behavior.
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