# 2.2 Partial Differential Equations

## 2.2.4 Characteristics for One-Dimensional Burgers' Equation

Measurable Outcome 2.1, Measurable Outcome 2.2, Measurable Outcome 2.5

Consider the one-dimensional Burgers' equation 2.17. What is the equation for the characteristic?

Exercise 1
&nbsp; \(\frac{dx}{dt}=u\) &nbsp;
&nbsp; \(\frac{dx}{dt}=2u\) &nbsp;
&nbsp; \(\frac{dx}{dt}=u^2\) &nbsp;
&nbsp; \(\frac{dx}{dt}=\frac{1}{2}u^2\) &nbsp;

Answer: Following the explanation above, we see that for the Burgers' equation, we can obtain \(\frac{dU}{dt}=0\) if we set \(\frac{dx}{dt}=u\), which gives the characteristic.