35,651 research outputs found
Three-dimensional Curve Motions Induced by the Modified Korteweg-de Vries Equation
We have constructed one-phase quasi-periodic solutions of the curve equation
induced by the mKdV equation. The solution is expressed in terms of the
elliptic functions of Weierstrass. This solution can describe curve dynamics
such as a vortex filament with axial velocity embedded in an incompressible
inviscid fluid. There exist two types of curves (type-A, type-B) according to
the form of the main spectra of the finite-band integrated solution. Our
solution includes various filament shapes such as the Kelvin-type wave, the
rigid vortex, plane curves, closed curves, and the Hasimoto one-solitonic
filament.Comment: 26 pages, 4 figure
Sine-Gordon Soliton on a Cnoidal Wave Background
The method of Darboux transformation, which is applied on cnoidal wave
solutions of the sine-Gordon equation, gives solitons moving on a cnoidal wave
background. Interesting characteristics of the solution, i.e., the velocity of
solitons and the shift of crests of cnoidal waves along a soliton, are
calculated. Solutions are classified into three types (Type-1A, Type-1B,
Type-2) according to their apparent distinct properties.Comment: 11 pages, 5 figures, Contents change
Non-local Wess-Zumino Model on Nilpotent Noncommutative Superspace
We investigate the theory of the bosonic-fermionic noncommutativity,
, and the Wess-Zumino model
deformed by the noncommutativity. Such noncommutativity links well-known
space-time noncommutativity to superspace non-anticommutativity. The
deformation has the nilpotency. We can explicitly evaluate noncommutative
effect in terms of new interactions between component fields. The interaction
terms that have Grassmann couplings are induced. The noncommutativity does
completely break full supersymmetry to
theory in Minkowski signature. Similar to the space-time noncommutativity, this
theory has higher derivative terms and becomes non-local theory. However this
non-locality is milder than the space-time noncommutative field theory. Due to
the nilpotent feature of the coupling constants, we find that there are only
finite number of Feynman diagrams that give noncommutative corrections at each
loop order.Comment: Latex, 16 pages, 2 figures, typos corrected, some references and
comments on auxiliary field added, a figure replaced, English refine
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