@article{f136b9869bb84863aa909f89fbe0a9cd,
title = "Compactons and their variational properties for degenerate kdv and nls in dimension 1",
abstract = "We analyze the stationary and traveling wave solutions to a family of degenerate dispersive equations of KdV-and NLS-type. In stark contrast to the standard soliton solutions for nondegenerate KdV and NLS equations, the degeneracy of the elliptic operators studied here allows for compactly supported steady or traveling states. As we work in 1 dimension, ODE methods apply; however, the models considered have formally conserved Hamiltonian, Mass, and Momentum functionals, which allow for variational analysis as well.",
author = "Pierre Germain and Benjamin Harrop-Griffiths and Marzuola, {Jeremy L.}",
note = "Funding Information: The first author was supported by the NSF grant DMS-15010. The second author was supported by a Junior Fellow award from the Simons Foundation. The third author was supported in part by U.S. NSF Grants DMS-1312874 and DMS-1352353. The authors thank John Hunter for very helpful conversations about degenerate NLS models at the beginning of the project. Also, the authors are grateful to Rupert Frank for discussions related to energy minimizers, in particular bringing to our attention the reference [28]. These discussions were initiated at the Mathematisches Forschungsinstitut Oberwolfach Funding Information: Received August 16, 2018, and, in revised form, January 29, 2019. 2010 Mathematics Subject Classification. Primary 35Q53, 35Q55. The first author was supported by the NSF grant DMS-15010. The second author was supported by a Junior Fellow award from the Simons Foundation. The third author was supported in part by U.S. NSF Grants DMS–1312874 and DMS-1352353. Email address: pgermain@cims.nyu.edu Email address: benjamin.harrop-griffiths@cims.nyu.edu Email address: marzuola@math.unc.edu Publisher Copyright: {\textcopyright} 2019 Brown University.",
year = "2020",
doi = "10.1090/QAM/1538",
language = "English (US)",
volume = "78",
pages = "1--32",
journal = "Quarterly of Applied Mathematics",
issn = "0033-569X",
publisher = "American Mathematical Society",
}