The inhomogeneous extension of equations of the reaction–diffusion type is investigated by means of the covariant prolongation structures theory. We construct the sl(2, R) × R(ρ(t)) prolongation structure for an inhomogeneous equation of the reaction–diffusion type and give the corresponding AKNS-type equations and the Bäcklund transformation.
A new simple low-cost technique for fabricating micro-gaps of less than 50 µm in copper electrodes is reported, which combines conventional screen printing of copper paste and intense pulsed light (IPL) sintering. The micro-gap is created via a two-step IPL sintering. First, a continuous printed copper stripe is half sintered along its length with another half blocked by an opaque mask. Then, the second sintering is performed over the entire length of copper stripe with the opaque mask removed. At the joint between two sintering steps, a micro-gap is formed across the copper stripe due to thermal contraction of underlying polyethylene terephthalate substrate. The width of copper micro-gaps can be adjusted by IPL energy. Simple light emitting diode circuits have been made by the micro-gap electrodes, demonstrating its feasibility for practical applications.
We present the bilinear equivalence expression of a (2+1)-dimensional integrable equation of a classical spin system. Based on this, we construct its single-soliton solutions and two-soliton solutions by Hirota's bilinear method. Meanwhile we show the evolution and propagation manners of two-solitons of the spin system graphically.
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