TY - JOUR
T1 - Compactons and their variational properties for degenerate kdv and nls in dimension 1
AU - Germain, Pierre
AU - Harrop-Griffiths, Benjamin
AU - Marzuola, Jeremy L.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
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U2 - 10.1090/QAM/1538
DO - 10.1090/QAM/1538
M3 - Article
AN - SCOPUS:85083451988
VL - 78
SP - 1
EP - 32
JO - Quarterly of Applied Mathematics
JF - Quarterly of Applied Mathematics
SN - 0033-569X
M1 - 1538
ER -