open access

https://hdl.handle.net/2115/100312

NON-POLYNOMIAL CONSERVED QUANTITIES FOR ODE SYSTEMS AND THEIR APPLICATION TO THE LONG-TIME BEHAVIOR OF SOLUTIONS TO CUBIC NLS SYSTEMS

英語

conservation laws

2026-06-15

American Mathematical Society

Transactions of the American Mathematical Society

379(9)

6117-6144

In this paper, we investigate the asymptotic behavior of small solutions to the initial value problem for a system of cubic nonlinear Schro & uml;dinger equations (NLS) in one spatial dimension. We identify a new class of NLS systems for which the global boundedness and asymptotics of small solutions can be established, even in the absence of any effective conserved quantity. The key to this analysis lies in utilizing conserved quantities for the reduced ordinary differential equation systems derived from the original NLS systems. In [arXiv:2412.00413], the first author investigated conserved quantities expressed as quartic polynomials. In contrast, the conserved quantities considered in the present paper are of a different type and are not necessarily polynomials.

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Accepted Manuscript

Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International

First published in Trans. Amer. Math. Soc. in v.379 n.9 (June 2026) , published by the American Mathematical Society. © 2026 American Mathematical Society.

0002-9947

1088-6850