Timeline for Existence of non-constant solutions for this equations
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 5, 2016 at 6:32 | vote | accept | Amir Baghban | ||
| Apr 5, 2016 at 6:32 | comment | added | Amir Baghban | I'm so sorry. I had some mistakes in my calculations. You're right. | |
| Apr 4, 2016 at 17:43 | comment | added | Robert Bryant | @Solar: I did the same thing, but using Maple to check the calculations, and I found that the pair $\bigl(u(x,y),v(x,y)\bigr)$ does solve the equation, so I don't know what you are doing wrong. | |
| Apr 4, 2016 at 16:21 | comment | added | Amir Baghban | Well, I will put the given $z=u+iv$ (in the Example) in the Equation $\frac{\partial z}{\partial x^l}+z \frac{\partial z}{\partial y^l}=0$. Yes, I know you took $x,y$ from $\mathbb{R}^n$. | |
| Apr 4, 2016 at 16:08 | comment | added | Robert Bryant | @Solar: Then you have a mistake in your equations, because the $u(x,y)$ and $v(x,y)$ as given in the Example do satisfy your given equations. You do understand that, in my notation, I am using $x = (x^1,\ldots,x^n)$ and $y = (y^1,\ldots,y^n)$ as vectors in $\mathbb{R}^n$, right? | |
| Apr 4, 2016 at 14:55 | comment | added | Amir Baghban | I checked the Example but the stated $u(x,y)$ and $v(x,y)$ in the Example don't satisfy in the sufficient and necessary Equations for the integrability of $J_{\delta,\beta}$. | |
| Apr 4, 2016 at 4:51 | vote | accept | Amir Baghban | ||
| Apr 4, 2016 at 13:04 | |||||
| Apr 1, 2016 at 17:37 | comment | added | Robert Bryant | @Solar: Sorry, I don't understand. What do you mean by 'the variable $z = u + i\,v$ does a role'? What is 'it' in "Is it right?"? I'm confused by your comment. Certainly, by $i$, I mean $\sqrt{-1}$. | |
| Apr 1, 2016 at 17:17 | comment | added | Amir Baghban | I think the variable $z=u+iv$ does a role as well as $i=\sqrt{-1}$. Is it right? I'm confused by this. | |
| Mar 31, 2016 at 20:52 | history | edited | Robert Bryant | CC BY-SA 3.0 |
Corrected an inadvertent switch of x and y throughout the answer after (1)
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| Mar 31, 2016 at 15:20 | history | edited | Robert Bryant | CC BY-SA 3.0 |
Fixed a typo in the formula for v(x,y) at the end.
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| Mar 31, 2016 at 14:29 | history | edited | Robert Bryant | CC BY-SA 3.0 |
Fixed a minor mistake caused by forgetting the double value of the square root
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| Mar 31, 2016 at 13:30 | history | answered | Robert Bryant | CC BY-SA 3.0 |