New nonlinear instability for scalar fields

In this Letter, we introduce the nonlinear partial differential equation ${\ensuremath{\partial}}_{\ensuremath{\tau}}^{2}\ensuremath{\pi}\ensuremath{\propto}(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nabla}}\ensuremath{\pi}{)}^{2}$ showing a new type of instability. Such equations appear in effective field theory (EFT) dark energy for $k$-essence model as well many other theories based on EFT formalism. We demonstrate occurrence instability cosmological context using relativistic $N$-body code, and study it mathematically $3+1$ dimensions within spherical symmetry. show that term dominates low speed sound limit where some important linear terms are suppressed.