A partial differential equation is said to have a symmetry transformation or symmetry if u0(x, t) = U(x, t, u(X(x, t, u),T(x, t, u))) is a solution given that u(x, t) is. In other words, a symmetry transformation maps solutions of an equation to solutions of the same equation.
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A solution A contains a set of inter- nal symmetries Σ (or equivalently Σ are internal symmetries within the solution) iff A contains σ for every σ ∈ Σ.
Nov 26, 2013 · It is not in general true that a solution to a symmetric problem must itself be symmetric. For example: Minimize x4−2x2.
A local Lie group of transformations G is called a symmetry group of the system of partial differential equations (1) if ¯f= g · f is a solution whenever f is.
Feb 9, 2011 · Symmetry in the context of an ODE refers to the invariance of the equation under certain transformations. In other words, a symmetric ODE will ...
PDEtools SymmetrySolutions computes the group invariant (point symmetry) solutions for a given PDE system Calling Sequence Parameters Description Examples ...
May 18, 2015 · Spontaneous symmetry breaking requires more than two distinct solutions to a system of equations, because there are often physical ...
Symmetry defines that the shape is identical on both sides when it is divided by a line. The symmetry of different shapes, regular or irregular.
Definition A symmetry of a given ODE is a locally-defined diffeomorphism, Γ, that maps the set of all solutions to itself. (Consequently, every solution is ...
Jul 3, 2010 · We define the concept of an internal symmetry. This is a symmety within a solution of a constraint satisfaction problem. We compare this to ...