论文标题
一般天上方程式中的线性叠加
Linear superposition in the general heavenly equation
论文作者
论文摘要
显然，在存在非线性的情况下，线性叠加原理不能完全确定为一般原理，并且乍一看，没有期望它甚至可以容纳近似。在这封信中表明，不同非线性效应的平衡描述了非线性系统中可能发生的线性叠加。天堂方程在几个科学领域都具有重要意义，尤其是在相对性，重力，田间理论和流体动力学方面。揭示了一种特殊类型的隐式冲击波解决方案，具有三维的一般天堂方程的二维任意功能。将二维任意函数限制为某些类型的一维任意函数，发现非线性效应可以平衡，以使“不可能”的线性叠加解决方案可以非繁琐地构成一般天堂方程的新解决方案。
Evidently, the linear superposition principle can not be exactly established as a general principle in the presence of nonlinearity, and, at the first glance, there is no expectation for it to hold even approximately. In this letter, it is shown that the balance of different nonlinear effects describes what linear superpositions may occur in nonlinear systems. The heavenly equations are of significance in several scientific fields, especially in relativity, gravity, field theory, and fluid dynamics. A special type of implicit shock wave solution with three two-dimensional arbitrary functions of the general heavenly equation is revealed. Restrict the two-dimensional arbitrary functions to some types of one-dimensional arbitrary functions, it is found that the nonlinear effects can be balanced such that the "impossible" linear superposition solutions can be nontrivially constituted to new solutions of the general heavenly equation.
