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- Toda_lattice abstract "The Toda lattice, introduced by Morikazu Toda (1967), is a simple model for a one-dimensional crystalin solid state physics. It is given by a chain of particles with nearest neighbor interactiondescribed by the equations of motionwhere is the displacement of the -th particle from its equilibrium position,and is its momentum (mass ).The Toda lattice is a prototypical example of a completely integrable system with soliton solutions. To see this one uses Flaschka's variablessuch that the Toda lattice readsThen one can verify that the Toda lattice is equivalent to the Lax equationwhere [L, P] = LP - PL is the commutator of two operators. The operators L and P, the Lax pair, are linear operators in the Hilbert space of square summable sequences given byThe matrix has the property that its eigenvalues are invariant in time. These eigenvalues constitute independent integrals of motion, therefore the Toda lattice is completely integrable.In particular, the Toda lattice can be solved by virtue of the inverse scattering transform for the Jacobi operator L. The main result implies that arbitrary (sufficiently fast) decaying initial conditions asymptotically for large t split into a sum of solitons and a decaying dispersive part.".
- Toda_lattice wikiPageExternalLink TodaLattice.html.
- Toda_lattice wikiPageExternalLink Toda.html.
- Toda_lattice wikiPageExternalLink toda.html.
- Toda_lattice wikiPageID "3240033".
- Toda_lattice wikiPageRevisionID "570808135".
- Toda_lattice authorlink "Morikazu Toda".
- Toda_lattice first "Morikazu".
- Toda_lattice hasPhotoCollection Toda_lattice.
- Toda_lattice last "Toda".
- Toda_lattice year "1967".
- Toda_lattice subject Category:Exactly_solvable_models.
- Toda_lattice subject Category:Solitons.
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- Toda_lattice comment "The Toda lattice, introduced by Morikazu Toda (1967), is a simple model for a one-dimensional crystalin solid state physics. It is given by a chain of particles with nearest neighbor interactiondescribed by the equations of motionwhere is the displacement of the -th particle from its equilibrium position,and is its momentum (mass ).The Toda lattice is a prototypical example of a completely integrable system with soliton solutions.".
- Toda_lattice label "Toda lattice".
- Toda_lattice label "Toda-Gitter".
- Toda_lattice label "Цепочка Тоды".
- Toda_lattice sameAs Toda-Gitter.
- Toda_lattice sameAs 도다_격자.
- Toda_lattice sameAs m.0661n15.
- Toda_lattice sameAs Q572090.
- Toda_lattice sameAs Q572090.
- Toda_lattice sameAs Toda_lattice.
- Toda_lattice wasDerivedFrom Toda_lattice?oldid=570808135.
- Toda_lattice isPrimaryTopicOf Toda_lattice.