Compactons and their variational properties for degenerate KdV and NLS in dimension 1
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 non …
equations of KdV and NLS-type. In stark contrast to the standard soliton solutions for non …
Existence and stability of solitons for the nonlinear Schrödinger equation on hyperbolic space
H Christianson, JL Marzuola - Nonlinearity, 2009 - iopscience.iop.org
Hyperbolic solitons Page 1 Nonlinearity Existence and stability of solitons for the nonlinear
Schrödinger equation on hyperbolic space To cite this article: Hans Christianson and Jeremy L …
Schrödinger equation on hyperbolic space To cite this article: Hans Christianson and Jeremy L …
[PDF][PDF] DISPERSIVE ESTIMATES FOR SCALAR AND MATRIX SCHRODINGER OPERATORS ON Hn
D Borthwick, JL Marzuola - arXiv preprint arXiv:1410.8829, 2014 - Citeseer
arXiv:1410.8829v3 [math.AP] 26 Nov 2014 Page 1 arXiv:1410.8829v3 [math.AP] 26 Nov
2014 DISPERSIVE ESTIMATES FOR SCALAR AND MATRIX SCHRODINGER …
2014 DISPERSIVE ESTIMATES FOR SCALAR AND MATRIX SCHRODINGER …
Gross--Pitaevskii Vortex Motion with Critically Scaled Inhomogeneities
We study the dynamics of vortices in an inhomogeneous Gross--Pitaevskii equation
i\partial_tu=Δu+1\overε^2(\rho_ε^2(x)-|u|^2). For a unique scaling regime |\rho_ε(x) …
i\partial_tu=Δu+1\overε^2(\rho_ε^2(x)-|u|^2). For a unique scaling regime |\rho_ε(x) …
[PDF][PDF] Traveling wave solutions to NLS and NLKG equations in non-Euclidean settings
M Taylor - Houston J. Math, 2016 - mtaylor.web.unc.edu
We study traveling wave solutions to nonlinear Schrödinger (NLS) and nonlinear Klein-
Gordon (NLKG) equations on a compact Riemannian manifold M, with a Killing field X …
Gordon (NLKG) equations on a compact Riemannian manifold M, with a Killing field X …
[PDF][PDF] Chapel Hill
KM Harris… - NC: University of North …, 2009 - Citeseer
Under the direction of Jeremy L. Marzuola Spectral renormalization, an iterative numerical
scheme for computing solitary waves of nonlinear waveguides established in [1], is …
scheme for computing solitary waves of nonlinear waveguides established in [1], is …
Nonlinear travelling waves on complete Riemannian manifolds
M Mukherjee - 2018 - projecteuclid.org
We study travelling wave solutions to nonlinear Schrödinger and Klein-Gordon equations on
complete Riemannian manifolds, which have a bounded Killing field X. For a natural class of …
complete Riemannian manifolds, which have a bounded Killing field X. For a natural class of …
Higher dimensional vortex standing waves for nonlinear Schrödinger equations
JL Marzuola, ME Taylor - Communications in Partial Differential …, 2016 - Taylor & Francis
We study standing wave solutions to nonlinear Schrödinger equations, on a manifold with a
rotational symmetry, which transform in a natural fashion under the group of rotations. We …
rotational symmetry, which transform in a natural fashion under the group of rotations. We …
A special class of nonlinear hypoelliptic equations on spheres
M Mukherjee - Nonlinear Differential Equations and Applications …, 2017 - Springer
We study nonlinear second-order equations of the form-Δ u+ X^ 2 u+ i λ X u+ σ u= K| u|^ p-1
u-Δ u+ X 2 u+ i λ X u+ σ u= K| u| p-1 u on S^ n S n with the usual round metric, where X is a …
u-Δ u+ X 2 u+ i λ X u+ σ u= K| u| p-1 u on S^ n S n with the usual round metric, where X is a …
A symplectic perspective on constrained eigenvalue problems
G Cox, JL Marzuola - Journal of Differential Equations, 2019 - Elsevier
The Maslov index is a powerful tool for computing spectra of selfadjoint, elliptic boundary
value problems. This is done by counting intersections of a fixed Lagrangian subspace …
value problems. This is done by counting intersections of a fixed Lagrangian subspace …