Logarithmic decay of solutions to coupled cubic nonlinear Schrödinger systems with defocusing dissipative nonlinearities

Yuwen Sun; Chunhua Li; Yuwen Sun; Chunhua Li

doi:10.3934/math.20261019

AIMS Mathematics

2026, Volume 11, Issue 8: 25390-25403. doi: 10.3934/math.20261019

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Research article

Logarithmic decay of solutions to coupled cubic nonlinear Schrödinger systems with defocusing dissipative nonlinearities

Yuwen Sun ,
Chunhua Li ^,

Department of Mathematics, College of Science, Yanbian University, No. 977 Gongyuan Road, Yanji City, Jilin Province, 133002, China

Received: 20 April 2026 Revised: 22 June 2026 Accepted: 06 July 2026 Published: 17 August 2026
MSC : 35B40, 35Q55

We investigate the time-decay estimates for solutions to the Cauchy problem for a system of two coupled cubic nonlinear Schrödinger equations in one space dimension. Without any size restriction on the initial data, we prove the global existence and uniqueness of solutions in the defocusing dissipative case. The main result shows that the $ L^{2} $-norm of the solution decays at the rate $ O\big((\log(2+t))^{-1/3}\big) $ as $ t\to+\infty $.
Citation: Yuwen Sun, Chunhua Li. Logarithmic decay of solutions to coupled cubic nonlinear Schrödinger systems with defocusing dissipative nonlinearities[J]. AIMS Mathematics, 2026, 11(8): 25390-25403. doi: 10.3934/math.20261019

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Abstract

We investigate the time-decay estimates for solutions to the Cauchy problem for a system of two coupled cubic nonlinear Schrödinger equations in one space dimension. Without any size restriction on the initial data, we prove the global existence and uniqueness of solutions in the defocusing dissipative case. The main result shows that the $ L^{2} $-norm of the solution decays at the rate $ O\big((\log(2+t))^{-1/3}\big) $ as $ t\to+\infty $.

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