L2-properties for linearized KdV equation around small solutions

Masaki Kawamoto

doi:10.55937/sut/1599942864

June 2020

L^2

-properties for linearized KdV equation around small solutions

Masaki Kawamoto

Author Affiliations +

SUT J. Math. 56(1): 1-19 (June 2020). DOI: 10.55937/sut/1599942864

Abstract

We consider the asymptotic behavior of a small solution to the linearized KdV equation. By rewriting this equation as a Hamiltonian system, the deduced Hamiltonian has unbounded, non-symmetric, and time-dependent potential. In this paper, we show the stableness of this solution to a linearized KdV equation in the $L^2$ sense and the decay estimates by analyzing this system.

Acknowledgement

The author would like to thank the anonymous referee for the careful reading of the manuscript and for useful suggestions.

Citation

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Masaki Kawamoto. " $L^2$ -properties for linearized KdV equation around small solutions." SUT J. Math. 56 (1) 1 - 19, June 2020. https://doi.org/10.55937/sut/1599942864