How to solve this nonlinear partial differential equation? $$\displaystyle\frac{\partial^2}{\partial x^2} f(x,t) +b \frac{\partial^2}{\partial x^2} f(x,t) \cdot \frac{\partial^2}{\partial t^2} f(x,t) + a = 0,$$ where $a,b$ are constant.
how to solve this nonlinear partial differential equation?
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ordinary-differential-equations
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0Can someone experienced in LaTeX edit this to use proper format? – 2011-03-26
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0Does $\left(\frac{\partial}{\partial x}\right)^2$ mean the second partial? – 2011-03-26
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1@Theo: If it is inside `$$...$$`, it's already in displaystyle... – 2011-03-26
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0@aniket: I tried to texify your source, I hope I haven't messed it up. @Arturo: my mistake I clicked on submit too early and thanks for the remark about `\displaystyle`. The original source said `(d/dx)^2`. – 2011-03-26
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0@aniket: no problem, but you should learn it yourself as soon as possible. It's not that hard :). More importantly: Could you please give some context? Where does the problem come from and what have you tried to do? – 2011-03-26
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0@aniket: partial sounds bad, nonlinear partial even worse. Are you searching for a solution or all solutions? (all solutions might be hopeless) – 2011-03-26
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0I think we should give this problem a better go, or at least explain a bit more about the difficulty we are really facing with this type of problem instead of breaking it down to something solvable but not really representative of $f_{xx}+bf_{xx}f_{tt}+a=0$. – 2012-05-20