On the Unique Continuation Property for a Coupled System of Third-order Nonlinear Schrodinger Equations

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Published: 2023-10-02

DOI: 10.56557/ajomcor/2023/v30i48400

Page: 42-62


Yue Zhou *

School of Mathematical Sciences, Sichuan Normal University, Chengdu, 610068, China.

Jie Yang

School of Mathematical Sciences, Sichuan Normal University, Chengdu, 610068, China.

*Author to whom correspondence should be addressed.


Abstract

In this paper, we study the unique continuation properties for a coupled system of third-order nonlinear Schrodinger equations and show the Carleman estimates of Land L(p > 2) types, as well as exponential decay properties of the solutions. As a consequence we obtain that if (\(\mathit{u}\), \(\mathit{w}\)) = (\(\mathit{u}\)(\(\mathit{x}\), \(\mathit{t}\)), \(\mathit{w}\)(\(\mathit{x}\), \(\mathit{t}\))) is a suffciently smooth solution of the system such that there exists \(\mathit{l}\) \(\in\) \(\mathbb{R}\) with supp \(\mathit{u}\)(.,tj) \(\subseteq\)(\(\mathit{l}\), \(\infty\)) (\(\mathit{or}\)(-\(\infty\), \(\mathit{l}\))) and supp \(\mathit{w}\)(.,tj) \(\subseteq\)(\(\mathit{l}\), \(\infty\)) (\(\mathit{or}\)(-\(\infty\), \(\mathit{l}\))), for \(\mathit{j}\) = 1,2 (t1 \(\neq\) t2), then \(\mathit{u}\) \(\equiv\) 0 and \(\mathit{w}\) \(\equiv\) 0.

Keywords: Schrodinger equations, compact support, Carleman estimates, unique continuation


How to Cite

Zhou, Y., & Yang, J. (2023). On the Unique Continuation Property for a Coupled System of Third-order Nonlinear Schrodinger Equations. Asian Journal of Mathematics and Computer Research, 30(4), 42–62. https://doi.org/10.56557/ajomcor/2023/v30i48400

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