We consider the hyperboloidal initial value problem for the cubic focusing wave equation
Without symmetry assumptions, we prove the existence of a codimension-4 Lipschitz manifold of initial data that lead to global solutions in forward time which do not scatter to free waves. More precisely, for any , we construct solutions with the asymptotic behavior
as , where and .
"Nondispersive decay for the cubic wave equation." Anal. PDE 7 (2) 461 - 495, 2014. https://doi.org/10.2140/apde.2014.7.461