Timeline for Theorems that tell if an explicit analytical solution is possible for nonlinear PDEs
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 2, 2016 at 1:13 | comment | added | littlelittlelittle | If we know that an equation has explicit solutions (for example there is a special explicit solution by observation), how could we find the general form of all explicit solutions? | |
| Nov 1, 2016 at 20:50 | comment | added | Robert Bryant | Darboux' Method does not always succeed. For example, for the equation $z_{xy} = z$, Lie showed that Darboux' method does not succeed in finding an explicit solution. In fact, even for linear equations of the form $z_{xy} = \lambda(x,y) z$ (where $\lambda(x,y)$ is a given function on the domain in question), it is nontrivial to determine the $\lambda$ so that the equation is solvable by the method of Darboux. | |
| Nov 1, 2016 at 19:37 | comment | added | littlelittlelittle | In general is there a way to find the explicit solution using Darboux's method? | |
| Mar 5, 2016 at 8:56 | vote | accept | Alan | ||
| Aug 23, 2015 at 19:41 | history | edited | Robert Bryant | CC BY-SA 3.0 |
added 302 characters in body
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| Aug 23, 2015 at 19:35 | history | answered | Robert Bryant | CC BY-SA 3.0 |