The movement of any object has a certain natural law, and the studies and solutions to many natural laws boil down to the problem of mathematical physics equations. Many important physical situations such as fluid flows, plasma physics, and solid state physics have been described by the Korteweg-de Vries (KdV)-type models. In this article, the (2+1)-dimensional KdV equation is presented. By using the Hirota’s bilinear form and the extended Ansätz function method, we obtain new exact periodic cross-kink wave solutions for the (2+1)-dimensional KdV equation. With the aid of symbolic computation, the properties for these exact periodic cross-kink wave solutions are shown with some figures.

Under investigation is a generalized Kadomtsev–Petviashvili equation with variable coefficients, which describes the long water waves and small-amplitude surface waves with weak nonlinearity, weak dispersion and weak perturbation in fluid mechanics. Stripe solitons and lump solutions are obtained by proposing an improved positive quadratic function based on Hirota’s bilinear form and symbolic computation. The dynamical properties of the obtained solutions are demonstrated in some 3D and contour plots by setting the values of the parameters.

Si Shen Wan (SSW) is used to effectively treat ulcerative colitis (UC) as a formula of traditional Chinese medicine. To explore the mechanism of SSW-inhibited apoptosis of colonic epithelial cell, the study observed mRNA expression of apoptosis-related molecules in p38 MAPK signal pathway in colonic mucosa in colitis mice treated with SSW. Experimental colitis was induced by 2,4,6-trinitrobenzene sulfonic acid (TNBS) in mice; meanwhile, the mice were administrated daily either SSW (5 g/kg) or p38 MAPK inhibitor (2 mg/kg) or vehicle (physiological saline) for 10 days. While microscopical evaluation was observed, apoptosis rate of colonic epithelial cell and mRNA expression of apoptosis-related molecules were tested. Compared with colitis mice without treatment, SSW alleviated colonic mucosal injuries and decreased apoptosis rate of colonic epithelial cell, while the mRNA expressions of p38 MAPK, p53, caspase-3, c-jun, c-fos, Bax, and TNF- α were decreased in the colonic mucosa in colitis mice treated with SSW, and Bcl-2 mRNA and the ratio of Bcl-2/Bax were increased. The present study demonstrated that SSW inhibited mRNA expression of apoptosis-related molecules in p38 MAPK signal pathway to downregulate colonic epithelial cells apoptosis in colonic mucosa in mice with colitis.

In this paper, with symbolic computation, the generalized Kuramoto-Sivashinsky equation which describes the fluctuations of the position of a flame front, the motion of a fluid going down a vertical wall, or a spatially uniform oscillating chemical reaction in a homogeneous medium, is studied via the extended tanh-function method. By virtue of the extended tanh-function method, new exact solutions of this equation are presented. The restrictions on the parameters are also identified. It is shown that the extended tanh-function method is a competent and influential tool in solving nonlinear partial differential equations in mathematical physics.

This paper reports the scheme of terahertz (THz) wave generation on the basis of difference frequency generation in two-dimensional periodically structural Crystals pumped by CO2 laser. The two orthogonal periodic structures individually compensate for both the phase mismatch of the launched lasers and the generated THz wave. Quasi phase matching (QPM) was designed to satisfy the wave vector phase matching condition in two-dimensional periodical GaAs crystals. The parallel to the direction of the pump wave propagation grating period Λ1 and perpendicular to the direction of the pump wave propagation grating period Λ2 of two-dimensional periodical GaAs crystals at the 100-1000μm (0.3-3THz) range are investigated. The length of the parallel to the direction of the pump wave propagation grating period is 90.17 μm and the length of the perpendicular to the direction of the pump wave propagation grating period is 83.69μm in the two-dimensional collinear QPM scheme to generate a frequency of 1 THz wave pumped by CO2 laser. The result shown that the scheme of phase matching applies two-dimensional collinear quasi phase matching (QPM) is efficient to obtain high power conversion efficiency of THz wave.