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### The solution to the non-linear convection equation

The non-linear convection equation $$u_{t} +uu_{x}=0$$ admits implicit solutions of the form $$u=f(x-ut).$$ How does one interpret this solution intuitively? Is there an example of a solution of this ...
28 views

### Formation of patterns in instabilities according to the wavelength of instability

Do the wavelengths of the instability have an influence on the type of patterns that we are going to get? Meaning for example in 2D, if the unstable wavelengths are small with respect to the size of ...
85 views

I'm reading the book Chaos by James Gleick and came upon a certain excerpt in the chapter 'Strange Attractors'. I'm having a hard time understanding it (the merging of two surfaces part, in particular)...
519 views

### Nonlinear waves equations derivation from Navier-Stokes

In my professor's lecture notes, I came across the next approach of studying non-linear waves in fluids. So we have compressible Navier-Stokes and continuity equation in 1D and we assume adiabatic ...
90 views

### How to popularly describe typical features of a “non-linear system”

To quote Physics.SE tag definition: The term non-linear or nonlinear has several definitions but is generally used to describe a system that cannot be approximated by a superposition principle or ...
5k views

### Why can't the Navier Stokes equations be derived from first principle physics?

At the 109th UCLA Faculty Research lecture, Seth Putterman gave a talk on Sonoluminescence. During the lecture he emphasized that "The Navier Stokes equations cannot be derived from first principles [...
2k views

### Explanation of the waves on the water planet in the movie Interstellar?

We will ignore some of the more obvious issues with the movie and assume all other things are consistent to have fun with some of these questions. Simple [hopefully] Pre-questions: 1) If the water ...
685 views

### Can I use Runge-Kutta to solve these equations?

Edit: I'm going to give some more background and derivation to show how I got to these equations. I am basically following the derivation that is found in the appendix of the following paper: R.M. ...
1k views

### Viscous Burgers equation physical meaning

The viscous Burgers' equation: $$q_{t}+q\:q_{x}~=~\nu\:q_{xx}, \mbox{ where } \:\:\nu >0,$$ combines the nonlinear propagation of $q(x,t)$ and the diffusion. What is this equation for? (in ...