Wronskian Form Solutions for a Variable Coefficient Kadomtsev–Petviashvili Equation

Starting from a simple transformation, and with the aid of symbolic computation, we establish the relation- ship between the solution of a generalized variable coefficient Kadomtsev-Petviashvili （vKP） equation and the solution of a system of linear partial differential equations. According to this relation, we obtain Wronskian form solutions of the vKP equation, and further present N-soliton-like solutions for some degenerated forms of the vKP equation. Moreover, we also discuss the influences of arbitrary constants on the soliton and N-soliton solutions of the KPII equation.     

Similarity Solutions for Generalized Variable Coefficients Zakharov-Kuznetsov Equation under Some Integrability Conditions

In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov- Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal system seven basic fields are determined, and for every vector field in the optimal system the admissible forms of the coefficients are found and this also leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations eventually reduce to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions in most cases.     

The influence of cell geometry on the Godunov scheme applied to the linear wave equation

By studying the structure of the discrete kernel of the linear acoustic operator discretized with a Godunov scheme, we clearly explain why the behaviour of the Godunov scheme applied to the linear wave equation deeply depends on the space dimension and, especially, on the type of mesh. This approach allows us to explain why, in the periodic case, the Godunov scheme applied to the resolution of the compressible Euler or Navier–Stokes system is accurate at low Mach number when the mesh is triangular or tetrahedral and is not accurate when the mesh is a 2D (or 3D) cartesian mesh. This approach confirms also the fact that a Godunov scheme remains accurate when it is modified by simply centering the discretization of the pressure gradient.     

Research on flux-flow oscillators induced different types of pinning potentials

We have studied dynamics of Josephson vortices in strongly coupled long Josephson junctions stack, such as an intrinsic Josephson junction, by numerical simulations based on coupled sine–Gordon equations considering a periodic pinning potential. In this report, we investigate flux-flow oscillators induced two types of pinning potentials. One is magnetic periodic pinning potential, the other is periodic bias currents. Our results demonstrate that the periodic pinning potential can develop the generated power of flux-flow oscillator in certain condition.     

Dynamic simulations of the dipolar driven demagnetization process of magnetic multi-core nanoparticles

In this work, we investigate dynamically the dipolar driven demagnetization process of magnetic multi-core particles by solving the Landau-Lifshitz equation for single-domain particles distributed on a three-dimensional sphere. We analyze the relaxation time in respect to different geometry and material parameters. Further we show that the demagnetization times differ from the behaviour of a single magnetic sphere in the case of low damping. To explain these dynamics nanoparticular systems of different dimensions are investigated. We show that deviations can be attributed to a confinement of the relaxation dynamics to a lower dimensional submanifold of the k-space.     

New solitary wave solutions for nonlinear evolution equations

Three important nonlinear evolution equations are solved with the aid of the symbolic manipulation system.Maple,using the direct algebraic method proposed recently,We explicitly obtain several new solutions of physical interest in addition to rederiving all the known solutions.     

New exact solution structures and nonlinear dispersion in the coupled nonlinear wave systems

In this Letter, to further understand the role of nonlinear dispersion in coupled nonlinear wave systems in both real and complex fields, we study the coupled Klein–Gordon equations with nonlinear dispersion in real field (called CKG(m,n,k)$\mathrm{CKG}(m,n,k)$ equation) and (2+1)$(2+1)$-dimensional generalization of coupled nonlinear Schrödinger equation with nonlinear dispersion in complex field (called GCNLS(m,n,k)$\mathrm{GCNLS}(m,n,k)$ equation) via some transformations. As a consequence, some types of solutions are obtained, which contain compactons, solitary pattern solutions, envelope compacton solutions, envelope solitary pattern solutions, solitary wave solutions and rational solutions.     

A power law distribution in patients’ lengths of stay in hospital

The distribution of patients’ lengths of stay in English hospitals is measured by using routinely collected data from 11 years. It is found to be well approximated by a power law distribution spanning over more than three decades. To explain this observation, a theoretical resource allocation model is presented. It is based on iterative long-term scheduling of hospital beds, and its main assumption is that future beds are allocated preferentially. This represents a situation where different parts of the health care system compete for resources, with bargaining powers proportional to current resource levels.     

On the spurious eigenvalues for a concentric sphere in BIEM

In this paper, the null-field integral equation method is employed to study the occurring mechanism of spurious eigenvalues for a concentric sphere. By expanding the fundamental solution into degenerate kernels and expressing the boundary density in terms of spherical harmonics, all boundary integrals can be analytically determined. It is noted that our null-field integral formulation can locate the collocation point on the real boundary thanks to the degenerate kernel. In addition, the spurious eigenvalues are parasitized in the formulations while true eigensolutions are dependent on the boundary condition such as the Dirichlet or Neumann problem. By using the updating term and updating document of singular value decomposition (SVD) technique, true and spurious eigenvalues can be extracted out, respectively. Besides, true and spurious boundary eigenvectors are obtained in the right and left unitary vectors in the SVD structure of the influence matrices. This finding agrees with that of 2D cases.