Hey!

I am kind of new to mathematica so I don't know a lot of stuff...

So trying to put the question in context... I want to know if there is a way in Mathematica 9 to solve

**Nonlinear Second Order Parial Differential Equation?**

I understand that I cannot use

**DSolve **since its a Second Order PDE but even with

**NDSolve**, I keep getting errors..

My

**PDEs** are something like this:

fpde = (1 + (D[y[x, t], t])^2) (D[y[x, t], {x, 2}]) + (1 + (D[y[x, t], x])^2) (D[y[x, t], {t, 2}]) == 0;

i.e.

(1 + (

**d**y /

**d**t)^2 ) * (

**d2**y /

**d**x2)) + (1 + (

**d**y /

**d**x)^2 ) * (

**d2**y /

**d?**t2)) = 0

where y is a function of x and t.

I also give

**two boundary conditions** and

**one initial conditon** while using NDSolve

I have tried the following:

mysol = NDSolve[{fpde, y[0, t] == 0, y[2 Pi, t] == 0, y[x, Pi/4] == 0}, y, {x, 0, 2 Pi}, {t, 0, 2 Pi}]

Error : The number of constraints (1) (initial conditions) is not equal to the total differential order of the system plus the number of discrete variables (2).

mysol = NDSolve[{fpde, y[0, t] == 0, y[2 Pi, t] == 0, Derivative[1, 0][y][x, 2 Pi] == Tan[x]}, y, {x, 0, 2 Pi}, {t, 0, 2 Pi}]

Error: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable.

I can't figure out if my application of the command is incorrect or if a different approach is required to solve such PDEs.

**My objective is to get the numerical solution to such an equation.**Thanks a lot!