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@book {Lannes,1AUTHOR = {Lannes, David},2TITLE = {The Water Waves Problem: Mathematical Analysis and Asymptotics},3SERIES = {Mathematical Surveys and Monographs},4PUBLISHER = {American Mathematical Society},5ADDRESS = {Providence, RI},6YEAR = {2013},7ISBN = {9780821894705},8}91011@article {HJ2,12AUTHOR = {Hur, Vera Mikyoung and Johnson, Mathew A.},13TITLE = {Modulational instability in the {W}hitham equation for water waves},14JOURNAL = {Stud. Appl. Math.},15FJOURNAL = {Studies in Applied Mathematics},16VOLUME = {134},17YEAR = {2015},18NUMBER = {1},19PAGES = {120--143},20ISSN = {0022-2526},21MRCLASS = {35Q53 (35B10 35C07)},22MRNUMBER = {3298879},23MRREVIEWER = {Thierry Cazenave},24}2526@article {BF,27AUTHOR = {Benjamin, T. B. and Feir, J. E.},28TITLE = {The disintegration of wave trains on deep water. {P}art 1. {T}heory},29JOURNAL = {J. Fluid Mech.},30FJOURNAL = {Journal of Fluid Mechanics},31VOLUME = {27},32YEAR = {1967},33NUMBER = {3},34PAGES = {417--437},35ISSN = {0022-1120},36}3738@article{Benjamin1967,39AUTHOR={Benjamin, T. Brooke and Hasselmann, K},40TITLE={Instability of Periodic Wavetrains in Nonlinear Dispersive Systems [and Discussion]},41JOURNAL = {Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.},42FJOURNAL = {Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences},43VOLUME={299},44YEAR={1967},45NUMBER={1456},46PAGES={59--76},47ISSN = {1364-5021}48}4950@article {HJ3,51AUTHOR = {Hur, Vera Mikyoung and Johnson, Mathew A.},52TITLE = {Modulational instability in the {W}hitham equation with surface tension and vorticity},53JOURNAL = {Nonlinear Anal.},54FJOURNAL = {Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods},55VOLUME = {129},56YEAR = {2015},57PAGES = {104--118},58ISSN = {0362-546X},59MRCLASS = {Preliminary Data},60MRNUMBER = {3414922},61}6263@article{HP2,64AUTHOR={Hur, Vera Mikyoung and Pandey, Ashish Kumar},65TITLE={Modulational instability in a shallow water model},66JOURNAL={Preprint},67PAGES={1608.04685},68YEAR={2016}69}7071@incollection{BHJ,72AUTHOR={Bronski, Jared C. and Hur, Vera Mikyoung and Johnson, Mathew A.},73TITLE={Modulational instability in equations of {K}d{V} type},74BOOKTITLE={New Approaches to Nonlinear Waves},75EDITORS={Tobiscnh, Elena},76SERIES={Lecture Notes in Physics},77VOLUME={908},78YEAR={2016},79PAGES={83--133},80PUBLISHER={Springer International Publishing},81ADDRESS={Berlin, Germany}82}8384@book {K,85AUTHOR = {Kato, Tosio},86TITLE = {Perturbation theory for linear operators},87EDITION = {Second},88NOTE = {Grundlehren der Mathematischen Wissenschaften, Band 132},89PUBLISHER = {Springer-Verlag, Berlin-New York},90YEAR = {1976},91PAGES = {xxi+619},92MRCLASS = {47-XX},93MRNUMBER = {0407617 (53 \#11389)},94}9596@article{Hur-blowup,97AUTHOR = {Hur, Vera Mikyoung},98TITLE = {On the formation of singularities for surface water waves},99JOURNAL = {Commun. Pure Appl. Anal.},100FJOURNAL = {Communications on Pure and Applied Analysis},101VOLUME = {11},102YEAR = {2012},103NUMBER = {4},104PAGES = {1465--1474},105ISSN = {1534-0392},106MRCLASS = {35R11 (35B44 35Q53 35R37 76B15)},107MRNUMBER = {2900797},108MRREVIEWER = {Francesco Petitta},109}110111@article{Hur-breaking,112AUTHOR = {Hur, Vera Mikyoung},113TITLE={Wave breaking in the {W}hitham equation for shallow water},114JOURNAL={Preprint},115PAGES={arxiv:1506.04075},116YEAR={2015}117}118119@article{BJ1,120AUTHOR = {Bronski, Jared C. and Johnson, Mathew A.},121TITLE = {The modulational instability for a generalized {K}orteweg-de {V}ries equation},122JOURNAL = {Arch. Ration. Mech. Anal.},123FJOURNAL = {Archive for Rational Mechanics and Analysis},124VOLUME = {197},125YEAR = {2010},126NUMBER = {2},127PAGES = {357--400},128ISSN = {0003-9527},129MRCLASS = {35Q53 (35B10 35B35 35C07 76B25)},130MRNUMBER = {2660515 (2012f:35456)},131MRREVIEWER = {John Albert},132}133134135