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I'm a bit uncertain about the validity of my argument/approach to the following:

I'm trying to prove that the solution to a partial differential equation

[itex] \frac{\partial u(x,t)}{\partial t} + N[u(x,t)] = 0[/itex], where N is some nonlinear operator, CAN BE (not necessarily is) asymmetric about x=0. I do not know [itex] u(x,t) [/itex].

To that end, I've been examining the behavior of the system under the transformation [itex] x\to -x [/itex] (i.e. a reflection or inversion transformation) and can show that

[itex] \frac{\partial u(x,t)}{\partial t} + N[u(x,t)] \neq\frac{\partial u(-x,t)}{\partial t} + N[u(-x,t)], [/itex]

so that we do not expect u(x,t) = u(-x,t).

I am wondering if this is the best way to test this reflection symmetry. Also, if I can find the terms in the operator N that violate this symmetry, is it coherent to call these 'symmetry breaking' terms?

Any references to relevant resources would be appreciated,

Thanks!

Nick

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# Testing symmetry properties of nonlinear governing equations

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