31,349 research outputs found
Integrable dispersionless KdV hierarchy with sources
An integrable dispersionless KdV hierarchy with sources (dKdVHWS) is derived.
Lax pair equations and bi-Hamiltonian formulation for dKdVHWS are formulated.
Hodograph solution for the dispersionless KdV equation with sources (dKdVWS) is
obtained via hodograph transformation. Furthermore, the dispersionless
Gelfand-Dickey hierarchy with sources (dGDHWS) is presented.Comment: 15 pages, to be published in J. Phys. A: Math. Ge
The generalized Kupershmidt deformation for constructing new integrable systems from integrable bi-Hamiltonian systems
Based on the Kupershmidt deformation for any integrable bi-Hamiltonian
systems presented in [4], we propose the generalized Kupershmidt deformation to
construct new systems from integrable bi-Hamiltonian systems, which provides a
nonholonomic perturbation of the bi-Hamiltonian systems. The generalized
Kupershmidt deformation is conjectured to preserve integrability. The
conjecture is verified in a few representative cases: KdV equation, Boussinesq
equation, Jaulent-Miodek equation and Camassa-Holm equation. For these specific
cases, we present a general procedure to convert the generalized Kupershmidt
deformation into the integrable Rosochatius deformation of soliton equation
with self-consistent sources, then to transform it into a -type
bi-Hamiltonian system. By using this generalized Kupershmidt deformation some
new integrable systems are derived. In fact, this generalized Kupershmidt
deformation also provides a new method to construct the integrable Rosochatius
deformation of soliton equation with self-consistent sources.Comment: 21 pages, to appear in Journal of Mathematical Physic
On the Toda Lattice Equation with Self-Consistent Sources
The Toda lattice hierarchy with self-consistent sources and their Lax
representation are derived. We construct a forward Darboux transformation (FDT)
with arbitrary functions of time and a generalized forward Darboux
transformation (GFDT) for Toda lattice with self-consistent sources (TLSCS),
which can serve as a non-auto-Backlund transformation between TLSCS with
different degrees of sources. With the help of such DT, we can construct many
type of solutions to TLSCS, such as rational solution, solitons, positons,
negetons, and soliton-positons, soliton-negatons, positon-negatons etc., and
study properties and interactions of these solutions.Comment: 20 page
B\"{a}cklund transformations for high-order constrained flows of the AKNS hierarchy: canonicity and spectrality property
New infinite number of one- and two-point B\"{a}cklund transformations (BTs)
with explicit expressions are constructed for the high-order constrained flows
of the AKNS hierarchy. It is shown that these BTs are canonical transformations
including B\"{a}cklund parameter and a spectrality property holds with
respect to and the 'conjugated' variable for which the point
belongs to the spectral curve. Also the formulas of m-times
repeated Darboux transformations for the high-order constrained flows of the
AKNS hierarchy are presented.Comment: 21 pages, Latex, to be published in J. Phys.
The Degasperis-Procesi equation with self-consistent sources
The Degasperis-Procesi equation with self-consistent sources(DPESCS) is
derived. The Lax representation and the conservation laws for DPESCS are
constructed. The peakon solution of DPESCS is obtained.Comment: 15 page
Individual device active cooling for enhanced system-level power density and more uniform temperature distribution
This paper provides a method of individual device active cooling system to balance the temperature distribution of system-level power density. 3L-ANPC GaN inverter was used to test and prove the feasibility of it in using multi-level systems
Higher Order Potential Expansion for the Continuous Limits of the Toda Hierarchy
A method for introducing the higher order terms in the potential expansion to
study the continuous limits of the Toda hierarchy is proposed in this paper.
The method ensures that the higher order terms are differential polynomials of
the lower ones and can be continued to be performed indefinitly. By introducing
the higher order terms, the fewer equations in the Toda hierarchy are needed in
the so-called recombination method to recover the KdV hierarchy. It is shown
that the Lax pairs, the Poisson tensors, and the Hamiltonians of the Toda
hierarchy tend towards the corresponding ones of the KdV hierarchy in
continuous limit.Comment: 20 pages, Latex, to be published in Journal of Physics
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