The influence of anisotropic strain on the valence band structure and related properties, including excitonic transition energies, transition polarization selection rules, band-edge hole effective masses, and exciton reduced effective masses, of polar and nonpolar plane GaN are systematically investigated using the well-known k⋅p Hamiltonian approach. We re-examine the band deformation potentials D3 and D4, and interband hydrostatic deformation potentials a1 and a2, and find that they take the values 9.4, −4.7, −3.0, and −12.4 eV, respectively. In order to correctly interpret the optical properties of GaN, the spin-orbit coupling effect cannot be neglected. Our numerical calculations show that pure linear polarization light emissions and absorptions can be obtained. In addition, the two topmost valence subbands can be effectively separated to reduce the band-edge density of state by manipulating the strain states in GaN epilayers, which is favorable for laser diode design. Furthermore, the band-edge hole effective masses exhibit significant in-plane anisotropy and are sensitive to the residual strain, while the influence of the residual strain on the exciton reduced effective masses is relatively weak.

This paper is concerned with a multi-component Camassa-Holm system, which has been proven to be integrable and has peakon solutions. This system includes many one-component and two-component Camassa-Holm type systems as special cases. In this paper, we first establish the local well-posedness and a continuation criterion for the system, then we present several global existence or blow-up results for two important integrable two-component subsystems. Our obtained results cover and improve recent results in [25,36].

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This paper is concerned with a two-component integrable Camassa-Holm type system with arbitrary smooth function H. If the function H belongs to a set H (defined in Section 4), then we obtain the existence and uniqueness of global strong solutions and global weak solutions to the system. Our obtained results generalize and improve considerably recent results in [38, 39].