Geodesic
SPATIAL HAMILTONIAN IDENTITIES FOR NONLOCALLY COUPLED SYSTEMS
Forum of Mathematics, Sigma, Tome 6 (2018)

Voir la notice de l'article provenant de la source Cambridge University Press

We consider a broad class of systems of nonlinear integro-differential equations posed on the real line that arise as Euler–Lagrange equations to energies involving nonlinear nonlocal interactions. Although these equations are not readily cast as dynamical systems, we develop a calculus that yields a natural Hamiltonian formalism. In particular, we formulate Noether’s theorem in this context, identify a degenerate symplectic structure, and derive Hamiltonian differential equations on finite-dimensional center manifolds when those exist. Our formalism yields new natural conserved quantities. For Euler–Lagrange equations arising as traveling-wave equations in gradient flows, we identify Lyapunov functions. We provide several applications to pattern-forming systems including neural field and phase separation problems. 
@article{10_1017_fms_2018_22,
     author = {BENTE BAKKER and ARND SCHEEL},
     title = {SPATIAL {HAMILTONIAN} {IDENTITIES} {FOR} {NONLOCALLY} {COUPLED} {SYSTEMS}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {6},
     year = {2018},
     doi = {10.1017/fms.2018.22},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2018.22/}
}
TY  - JOUR
AU  - BENTE BAKKER
AU  - ARND SCHEEL
TI  - SPATIAL HAMILTONIAN IDENTITIES FOR NONLOCALLY COUPLED SYSTEMS
JO  - Forum of Mathematics, Sigma
PY  - 2018
VL  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1017/fms.2018.22/
DO  - 10.1017/fms.2018.22
LA  - en
ID  - 10_1017_fms_2018_22
ER  - 
%0 Journal Article
%A BENTE BAKKER
%A ARND SCHEEL
%T SPATIAL HAMILTONIAN IDENTITIES FOR NONLOCALLY COUPLED SYSTEMS
%J Forum of Mathematics, Sigma
%D 2018
%V 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1017/fms.2018.22/
%R 10.1017/fms.2018.22
%G en
%F 10_1017_fms_2018_22
BENTE BAKKER; ARND SCHEEL. SPATIAL HAMILTONIAN IDENTITIES FOR NONLOCALLY COUPLED SYSTEMS. Forum of Mathematics, Sigma, Tome 6 (2018). doi: 10.1017/fms.2018.22

Cité par Sources :