Construction of excited multi-solitons for the focusing 4D cubic wave equation

Consider the focusing 4D cubic wave equation∂ttu−Δu−u3=0,on(t,x)∈[0,∞)×R4. The main result states existence in energy space H˙1×L2 of multi-solitary waves where each traveling is generated by Lorentz transform from a specific excited state, with different but collinear speeds. state deduced non-degenerate sign-changing constructed Musso-Wei [34]. proof inspired techniques developed for 5D energy-critical equation and nonlinear Klein-Gordon similar context Martel-Merle [30] Côte-Martel [6]. difficulty originates strong interactions between solutions case compared to other dispersive wave-type models. To overcome difficulty, sharp understanding asymptotic behavior involved kernel their linearized operator needed.