432 research outputs found
The tanh and the sine-cosine methods for the complex modified K dV and the generalized K dV equations
AbstractThe complex modified K dV (CMK dV) equation and the generalized K dV equation are investigated by using the tanh method and the sine-cosine method. A variety of exact travelling wave solutions with compact and noncompact structures are formally obtained for each equation. The study reveals the power of the two schemes where each method complements the other
Electrical behaviour, characteristics and properties of anodic aluminium oxide films coloured by nickel electrodeposition
Porous anodic films on 1050 aluminium substrate were coloured by AC electrodeposition of nickel. Several experiments were performed at different deposition voltages and nickel concentrations in the electrolyte in order to correlate the applied electrical power to the electrical behaviour, as well as the characteristics and properties of the coatings. The content of nickel inside the coatings reached 1.67 g/m2, depending on the experimental conditions. According to the applied AC voltage in comparison with the threshold voltage Ut, the coating either acted only as a capacitor when U\Ut and, when U[Ut, the behaviour during the anodic and cathodic parts of the power sine wave was different. In particular, due to the semi-conducting characteristics of the barrier layer, additional oxidation of the aluminium substrate occurred during the anodic part of the electrical signal, whilst metal deposition (and solvent reduction) occurred during the cathodic part; these mechanisms correspond to the blocked and pass directions of the barrier layer/electrolyte junction, respectively
Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation
The aim of this paper is the accurate numerical study of the KP equation. In
particular we are concerned with the small dispersion limit of this model,
where no comprehensive analytical description exists so far. To this end we
first study a similar highly oscillatory regime for asymptotically small
solutions, which can be described via the Davey-Stewartson system. In a second
step we investigate numerically the small dispersion limit of the KP model in
the case of large amplitudes. Similarities and differences to the much better
studied Korteweg-de Vries situation are discussed as well as the dependence of
the limit on the additional transverse coordinate.Comment: 39 pages, 36 figures (high resolution figures at
http://www.mis.mpg.de/preprints/index.html
On the (Non)-Integrability of KdV Hierarchy with Self-consistent Sources
Non-holonomic deformations of integrable equations of the KdV hierarchy are
studied by using the expansions over the so-called "squared solutions" (squared
eigenfunctions). Such deformations are equivalent to perturbed models with
external (self-consistent) sources. In this regard, the KdV6 equation is viewed
as a special perturbation of KdV equation. Applying expansions over the
symplectic basis of squared eigenfunctions, the integrability properties of the
KdV hierarchy with generic self-consistent sources are analyzed. This allows
one to formulate a set of conditions on the perturbation terms that preserve
the integrability. The perturbation corrections to the scattering data and to
the corresponding action-angle variables are studied. The analysis shows that
although many nontrivial solutions of KdV equations with generic
self-consistent sources can be obtained by the Inverse Scattering Transform
(IST), there are solutions that, in principle, can not be obtained via IST.
Examples are considered showing the complete integrability of KdV6 with
perturbations that preserve the eigenvalues time-independent. In another type
of examples the soliton solutions of the perturbed equations are presented
where the perturbed eigenvalue depends explicitly on time. Such equations,
however in general, are not completely integrable.Comment: 16 pages, no figures, LaTe
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