# American Institute of Mathematical Sciences

January  2016, 21(1): 245-252. doi: 10.3934/dcdsb.2016.21.245

## Long-time behavior of solutions of the generalized Korteweg--de Vries equation

 1 ALHOSN University, Mathematics and Natural Sciences Department, PO Box 38772, Abu Dhabi

Received  August 2014 Revised  August 2015 Published  November 2015

In this paper, we study the large-time behavior of solutions to the initial-value problem for the generalized Korteweg--de Vries equation. We show that for initial data in some weighted space, the asymptotic behavior of the solution can be improved. In addition, we give the asymptotic profile of the fundamental solution of the linearized model. We extend and improve the results in [3] and [2].
Citation: Belkacem Said-Houari. Long-time behavior of solutions of the generalized Korteweg--de Vries equation. Discrete & Continuous Dynamical Systems - B, 2016, 21 (1) : 245-252. doi: 10.3934/dcdsb.2016.21.245
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