# On uniqueness and decay of solution for Hirota equation - Mathematics > Analysis of PDEs

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Abstract: We address the question of the uniqueness of solution to the initial valueproblem associated to the equation \partial {t}u+i\alpha\partial^{2} {x}u+\beta \partial^{3} {x}u+i\gamma|u|^{2}u+\delta|u|^{2}\partial {x}u+\epsilon u^{2}\partial {x}\bar{u} = 0, \quad x,t \in \R,and prove that a certain decay property of the difference $u 1-u 2$ of twosolutions $u 1$ and $u 2$ at two different instants of times $t=0$ and $t=1$,is sufficient to ensure that $u 1=u 2$ for all the time.

Author: ** Xavier Carvajal, Mahendra Panthee**

Source: https://arxiv.org/