64,063 research outputs found
Multi loop soliton solutions and their interactions in the Degasperis-Procesi equation
In this article, we construct loop soliton solutions and mixed soliton - loop
soliton solution for the Degasperis-Procesi equation. To explore these
solutions we adopt the procedure given by Matsuno. By appropriately modifying
the -function given in the above paper we derive these solutions. We
present the explicit form of one and two loop soliton solutions and mixed
soliton - loop soliton solutions and investigate the interaction between (i)
two loop soliton solutions in different parametric regimes and (ii) a loop
soliton with a conventional soliton in detail.Comment: Published in Physica Scripta (2012
Reformulasi dari solusi -soliton untuk persamaan korteweg-de vries
Solusi 3-soliton dari persaxnaan Korteweg-de Vries (MI!) dapat diperoleh dengan Metode Hirota. Reformulasi solusi 3-soliton dinyatakan sebagai superposisi solusi masing-masing individu soliton. Sedangkan bentuk asymptotik solusi 3-soliton diperoleh melalui proses pelimitan terhadap parameter t. Pergeseran fase dari masing-masing individu soliton dibahas secara detail berdasarkan bentuk asymptotiknya. Dari analisis ditunjukkan bahwa soliton pertama selalu mengalami pergeseran fase (maju), soliton kedua mempunyai beberapa kemungkinan, yaitu tidak mengalami pergeseran fase, mengalami pergeseran fase maju, atau mengalami pergeseran fase mundur, dan soliton ketiga selalu mengalami pergeseran fase (mundur).
The solution of 3-soliton for Korteweg-de Vries (KdV) equation can be obtained by the Hirota Method. The reformulation of the 3-soliton solution was represented as the superposition of the solution of each individual soliton. Moreover, the asymptotic form of 3-soliton solution was obtained by limiting of the t parameter. The phase shift of each individual soliton are analysed in detail base its asymptotic form. The results of the analysis shown that the first soliton always have .a phase shift called forward, the second soliton have some possibility (there. .. is no phase shift, have a forward: phase shift, or have a backward phase shift), and for the third soliton always have a phase shift called backward.
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Non-BPS Solutions of the Noncommutative CP^1 Model in 2+1 Dimensions
We find non-BPS solutions of the noncommutative CP^1 model in 2+1 dimensions.
These solutions correspond to soliton anti-soliton configurations. We show that
the one-soliton one-anti-soliton solution is unstable when the distance between
the soliton and the anti-soliton is small. We also construct time-dependent
solutions and other types of solutions.Comment: 11 pages, minor correction
Soliton Turbulence in Shallow Water Ocean Surface Waves
We analyze shallow water wind waves in Currituck Sound, North Carolina and
experimentally confirm, for the first time, the presence of
in ocean waves. Soliton turbulence is an exotic form of nonlinear
wave motion where low frequency energy may also be viewed as a
, described theoretically by the soliton limit of the
Korteweg-deVries (KdV) equation, a
: Hence the phrase "soliton turbulence" is synonymous with "integrable
soliton turbulence." For periodic/quasiperiodic boundary conditions the
of KdV are exactly solvable by
(FGT), the basis of our data analysis. We find that large amplitude measured
wave trains near the energetic peak of a storm have low frequency power spectra
that behave as . We use the linear Fourier transform to
estimate this power law from the power spectrum and to filter
from the data. We apply FGT to determine the
and find that the low frequency region
is . The solitons have , a
, which supports our interpretation
of the data as soliton turbulence. From the
we are able to demonstrate that the solitons are
and .Comment: 4 pages, 7 figure
Soliton equations solved by the boundary CFT
Soliton equations are derived which characterize the boundary CFT a la Callan
et al. Soliton fields of classical soliton equations are shown to appear as a
neutral bound state of a pair of soliton fields of BCFT. One soliton amplitude
under the influence of the boundary is calculated explicitly and is shown that
it is frozen at the Dirichlet limit.Comment: 13 page
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