## Construction of two-bubble solutions for the energy-critical NLS.(English)Zbl 1375.35492

Summary: We construct pure two-bubbles for the energy-critical focusing nonlinear Schrödinger equation in space dimension $$N \geq 7$$. The constructed solution is global in (at least) one time direction and approaches a superposition of two stationary states both centered at the origin, with the ratio of their length scales converging to $$0$$. One of the bubbles develops at scale $$1$$, whereas the length scale of the other converges to $$0$$ at rate $$|t|^{-\frac{2}{N-6}}$$. The phases of the two bubbles form the right angle.

### MSC:

 35Q55 NLS equations (nonlinear Schrödinger equations) 35B40 Asymptotic behavior of solutions to PDEs 35C08 Soliton solutions
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### References:

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