# Hamilton Jacobi equation,

1. Sep 15, 2005

### eljose

Let be the S function being the action in physics S=S(x,y,z,t) satisfying the equation:

$$\frac{dS}{dt}+(1/2m)(\nabla{S})^{2}+V(x,y,z,t)=0$$

where V is the potential is there any solution (exact) to it depending on V?

2. Sep 16, 2005

### Dr Avalanchez

Implicit function theorem?

3. Dec 2, 2005

### Feynman

We can prove the existence and the unicity of the solution ,
What do you mean by$$\nabla{S})^{2}$$ is it the laplacian of S?
what is your boundary condition?is it Dirichlet or Neuman?

4. Dec 14, 2005

### Feynman

i m still wait your reponse

5. Dec 14, 2005

### incognitO

$$(\nabla S)^2=|\nabla S|^2 \qquad \hbox{the square gradient}$$

you can establish an equivalent system of ode's for your nonlinear problem and then aswer the questions for existence, unicity and solvability...
for more details check first chapter of Fritz John book.

6. Dec 19, 2005

### Feynman

In this case we can use the nonlinear semi group theory

7. Dec 20, 2005

### dextercioby

There are system of coordinates and forms of the potential function as to insure full separation of variables...See Landau's book on mechanics.

Daniel.