Dif.eq.(Wave dif.eq) Automodel

1. The problem statement, all variables and given/known data

Hi,

My problem:

Find automode l solution to

[itex]\frac{du}{dt}[/itex]=a²[itex]\frac{du}{dx}[/itex][itex]\frac{du}{dx}[/itex]

if u=y(x-ct)





2. Relevant equations

So its seems rather easy to get to the solution,if i substitute u inside the original equation.

Then i have diferental equation ,which i can solve.Solving is not the peoblem this time.



I do not understand what is automodel,could someone explain the difference between"normal" model and automodel? What kind of physical interpratation it has?





3. The attempt at a solution

1. The problem statement, all variables and given/known data







2. Relevant equations







3. The attempt at a solution

1. The problem statement, all variables and given/known data







2. Relevant equations







3. The attempt at a solution

1. The problem statement, all variables and given/known data







2. Relevant equations







3. The attempt at a solution

1. The problem statement, all variables and given/known data







2. Relevant equations







3. The attempt at a solution