Using a solution concept defined in the setting of a product of distributions, we consider the nonlinear equation f(t)u_t + (u²)_x = 0, where f is a continuous function. This equation can be regarded a generalization of Burgers inviscid equation and allows to study several kinds of interaction of δ-waves. If f(t) ≠ 0 for all t, collisions of δ-waves cannot exist. If f(t) = 0 for certain values of t, collisions of δ-waves may arise. In certain cases, the evolution of δ-waves under collision is similar to classical solitons collisions, for instance, in the Korteweg—de Vries equation. Phenomena of scattering, merging, annihilation and creation of Dirac masses are also possible in this setting. These results are easy to obtain essentially because, in our approach, the product of distributions is a distribution which does not depend on approximation processes. We include the main ideas concerning such products and several results obtained within this framework.

中文翻译：

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非线性模型中三角波的产生，An灭和相互作用：一种分布乘积方法

使用在分布积设置中定义的解决方案概念，我们考虑非线性方程f（t）u _t +（u ²）_x = 0，其中f是连续函数。该方程可以视为Burgers无粘性方程的推广，可以研究δ波的几种相互作用。如果对于所有t f（t）≠0 ，则δ波的碰撞将不存在。如果对于某些t值f（t）= 0 ，则δ发生碰撞-可能会出现波浪。在某些情况下，例如在Korteweg-de Vries方程中，碰撞下的δ波演化类似于经典的孤子碰撞。在这种情况下，狄拉克质量的散射，合并，an灭和创建现象也是可能的。这些结果很容易获得，因为在我们的方法中，分布的乘积是不依赖于近似过程的分布。我们包括有关此类产品的主要思想以及在此框架内获得的一些结果。