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

Published: 2023-10-02

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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