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 the...

We study sine-Gordon kink diffusion at finite temperature in the overdamped limit. By means of a general perturbative approach, we calculate the first- and second-order (in temperature) contributions to the diffusion coefficient. We compare our analytical predictions with numerical simulations. The good agreement allows us to conclude that, up to temperatures where kink-antikink nucleation proc...

Extending the gauge-invariance principle for τ functions of the standard bilinear formalism to the supersymmetric case, we define N=1 supersymmetric Hirota operators. Using them, we bilinearize SUSY KdV-type equations (KdV, Sawada-Kotera-Ramani, Hirota-Satsuma). The solutions for multiple collisions of super-solitons and extension to SUSY sine-Gordon are also discussed.

The matrix sine-Gordon theory, a matrix generalization of the well-known sine-Gordon theory, is studied. In particular, the A3-generalization where fields take value in SU(2) describes integrable deformations of conformal field theory corresponding to the coset SU(2)× SU(2)/SU(2). Various classical aspects of the matrix sine-Gordon theory are addressed. We find exact solutions, solitons and bre...

In this case the points 0k,, = are sin xkn are equidistributed in Weyl's sense . A non-negative measure da for which the array xkn (da) has the distribution function fl o(t) will be called an arc-sine measure . If du(x) = w(x) dx is absolutely continuous, we apply, replacing dca by w, the notations pn(W,x), yn (w), xkn(w) and call a non-negative w(x) an arc-sine weight if da(x) = w(x) dx is an ...

We investigated the noise levels in cell-attached patch capacitance recordings with a lock-in amplifier. The capacitance noise level decreases with increasing sine wave frequency up to 20-40 kHz. With a 20-mV rms sine wave the rms noise level above 8 kHz is <50 aF. With increasing sine wave amplitudes a further reduction down to 14 aF could be achieved. Capacitance measurements with a lock-in a...

SINEBase (http://sines.eimb.ru) integrates the revisited body of knowledge about short interspersed elements (SINEs). A set of formal definitions concerning SINEs was introduced. All available sequence data were screened through these definitions and the genetic elements misidentified as SINEs were discarded. As a result, 175 SINE families have been recognized in animals, flowering plants and g...