Lie algebra and differential equations

by MarkovMarakov
Tags: diff equation, lie algebra
MarkovMarakov is offline
Nov25-12, 07:07 PM
P: 34
I am having trouble understanding a section in these notes: . It is on page 3. Section 3 -- Discretization of the Korteweg-de Vries equation. I don't understand why [tex]V_4=x∂_x+3t∂_t-2u∂_u[/tex] generates a symmetry group of the KdV. I see that it generates the transformation
[tex](x',t',u')= (x\exp(\epsilon), 3t\exp(\epsilon), -2u\exp(\epsilon))[/tex]
So [tex]u'_{t'}-6u'u'_{x'}+u'_{x'x'x'}=-{2\over 3}u_t-24\exp(\epsilon)uu_x-2\exp(-2\epsilon)u_{xxx}[/tex] How does this vanish (so that we get symmetry) given that [itex]u[/itex] satisfies the KdV?
Phys.Org News Partner Science news on
Simplicity is key to co-operative robots
Chemical vapor deposition used to grow atomic layer materials on top of each other
Earliest ancestor of land herbivores discovered

Register to reply

Related Discussions
Interest in Linear algebra and Differential Equations? Academic Guidance 4
Differential Equations or Linear Algebra? Academic Guidance 7
Linear Algebra or Differential equations? Academic Guidance 6
linear algebra ordinary differential equations Calculus & Beyond Homework 11
Differential Equations vs Linear Algebra General Math 6