1-Soliton solution and conservation laws for the Jaulent-Miodekequation with power law nonlinearity
Abstract This paper obtains the 1-soliton solution of the Jaulent–Miodek equation with power law nonlinearity. The solitary wave ansatz is used to obtain the soliton solution to this equation. Subsequently, the conserved quantities are computed using the invariance and multiplier approach based on the well known result that the Euler–Lagrange operator annihilates the total divergence.
Cusp-like singular soliton solutions of Jaulent–Miodek equation using symbolic computation
In this paper, the sine–cosine method is employed to construct a series of exact solitary solutions to the celebrated Jaulent–Miodek equation. Solitons, anti-solitons and cusp-like singular solutions are obtained with the aid of symbolic computation.
Unidirectional hexagonal rare-earth disilicide nanowires on vicinal Si(100)-2×1
Rare-earth disilicide nanowires grown on vicinal Si(100) with a miscut of 2–2.5° toward the [110] azimuth at 600 °C were studied by scanning tunneling microscopy and compared with those grown on flat Si(001). In contrast to rare-earth disilicide nanowires grown on flat Si(100) surfaces, the nanowires grow unidirectionally along the [01̄1] direction of the vicinal Si(100) surface. Rare-earth disilicide nanowires form bundles composed of single nanowire units on both flat and vicinal surfaces. Yet, on the vicinal surface, the bundle width is comparable to the width of the terrace. The average nanowire length on the vicinal substrate is longer than that on the flat substrate. Scanning tunneling spectroscopy shows that the rare-earth disilicide nanowires have metallic properties.