Abstract

A method for generating solutions of the Burgers equation, which describe the interaction of waves in a nonlinear dissipative medium with a linearly growing wavefront, is proposed. The exact solutions describing these interactions and symmetry properties of the equation are used. It is shown that the rising wavefront is able to compete with the dissipation and compress the signal in time. On the contrary, the wavefront with the decreasing steepness “stretches” the signal.

中文翻译：

---

波前对耗散介质中非线性波的影响

摘要

提出了一种生成 Burgers 方程解的方法，该方程描述了非线性耗散介质中波与线性增长波前的相互作用。使用描述这些相互作用和方程对称性的精确解。结果表明，上升波前能够与耗散竞争并及时压缩信号。相反，陡度减小的波前会“拉伸”信号。