Sheng Zhang

To construct fractional rogue waves, this paper first introduces a conformable fractional partial derivative. Based on the conformable fractional partial derivative and its properties, a fractional Schrödinger equation with Lax integrability is then derived and first- and second-order fractional rogue wave solutions of which are finally obtained. The obtained fractional rogue wave solutions possess translational coordination, providing, to some extent, the degree of freedom to adjust the position of the rogue waves on the coordinate plane. It is shown that the obtained first- and second-order fractional rogue wave solutions are steeper than those of the corresponding NLS equation with integer-order derivatives. Besides, the time the second-order fractional rogue wave solution undergoes from the beginning to the end is also short. As for asymmetric fractional rogue waves with different backgrounds and amplitudes, this paper puts forward a way to construct them by modifying the obtained first- and second-order fractional rogue wave solutions.

Searching for integrable systems and constructing their exact solutions are of both theoretical and practical value. In this paper, Ablowitz–Kaup–Newell–Segur spectral problem and its time evolution equation are first generalized by embedding a new spectral parameter. Based on the generalized AKNS spectral problem and its time evolution equation, Lax integrability of a nonisospectral integrodifferential system is then verified. Furthermore, exact solutions of the nonisospectral integrodifferential system are formulated through the inverse scattering transform method. Finally, in the case of reflectionless potentials, the obtained exact solutions are reduced ton-soliton solutions. Whenn=1andn=2, the characteristics of soliton dynamics of one-soliton solutions and two-soliton solutions are analyzed with the help of figures.

© 2016 American Chemical Society.Layered transition metal chalcogenides with large spin orbit coupling have recently sparked much interest due to their potential applications for electronic, optoelectronic, spintronics, and valleytronics. However, most current understanding of the electronic structure near band valleys in momentum space is based on either theoretical investigations or optical measurements, leaving the detailed band structure elusive. For example, the exact position of the conduction band valley of bulk MoS2 remains controversial. Here, using angle-resolved photoemission spectroscopy with submicron spatial resolution, we systematically imaged the conduction/valence band structure evolution across representative chalcogenides MoS2, WS2, and WSe2, as well as the thickness dependent electronic structure from bulk to the monolayer limit. These results establish a solid basis to understand the underlying valley physics of these materials, and also provide a link between chalcogenide electronic band structure and their physical properties for potential valleytronics applications.