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Jendrej, Jacek

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

Anal. PDE 10, No. 8, 1923-1959 (2017).
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.

Cited in 9 Documents

MSC:

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

Keywords:

nonlinear Schrödinger equation; energy-critical; multisoliton
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\textit{J. Jendrej}, Anal. PDE 10, No. 8, 1923--1959 (2017; Zbl 1375.35492)
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