Energy Conservation for $p$-Adic and SFT String Equations

A conserved energy functional for the equations describing spatially homogeneous configurations of an open fermionic string tachyon field is constructed. For a special value of the model's parameter $q$, $q=0$, this functional gives conserved energy for a $p$-adic string tachyon ($p=3$). A conserved energy for equations describing interacting open and closed strings is presented in a special form that is a sum of functionals depending on open and closed string tachyon fields, respectively, which allows us to study the energy flow from open to closed strings.