Manuscript VII-A-ST@1 · VII-A-ST.tex · section · c39a67a3

The scalar assignment

Switching before variation › The scalar assignment · lines 594–608

VII-A-ST@1#eq:scalar-coeff

Fix a real smooth free scalar $P_{m} ϕ_{0} = 0$ with declared Cauchy data. Define

ϕ_{g} [γ; ϕ_{0}] u_{1, g} u_{2, g} = ϕ_{0} + κ u_{1, g} + κ^{2} u_{2, g} (mod κ^{3}), = - E_{m} V_{g} [h] ϕ_{0}, = E_{m} V_{g} [h] E_{m} V_{g} [h] ϕ_{0} - E_{m} W_{g} [h, k] ϕ_{0} .

Both positive-order coefficients have zero Cauchy data.

Displayed formulas in this passage

VII-A-ST@1#eq:scalar-coeff · line 598
$ϕ_{g} [γ; ϕ_{0}] u_{1, g} u_{2, g} = ϕ_{0} + κ u_{1, g} + κ^{2} u_{2, g} (mod κ^{3}), = - E_{m} V_{g} [h] ϕ_{0}, = E_{m} V_{g} [h] E_{m} V_{g} [h] ϕ_{0} - E_{m} W_{g} [h, k] ϕ_{0} .$