Approximate solution of the magneto-hydrodynamic flow over a nonlinear stretching sheet

The approximate solution of the magneto-hydrodynamic (MHD) boundary layer flow over a nonlinear stretching sheet is obtained by combining the Lie symmetry method with the homotopy perturbation method. The approximate solution is tabulated, plotted for the values of various parameters and compared with the known solutions. It is found that the approximate solution agrees very well with the known numerical solutions, showing the reliability and validity of the present work.     

一类非线性波动方程的势对称分类

先给出了含有一个任意函数的线性波动方程的古典和势对称的完全分类.然后,在此基础上给出了含有两个任意函数的一类非线性波动方程的两种情形势对称分类,得到了该方程的新势对称.在处理对称群分类问题的难点-求解确定方程组时我们提出了微分形式吴方法算法,克服了以往难于处理的困难.在整个计算过程中反复使用了吴方法,吴方法起到了关键的作用.     

New conservation laws obtained directly from symmetry action on a known conservation law

Two formulas are introduced to directly obtain new conservation laws for any system of partial differential equations from a known conservation law and admitted symmetries. The first formula maps any conservation law of a given system to the corresponding conservation law of the system obtained through a contact transformation. When the contact transformation is a symmetry of the given system, then the corresponding conservation law is a conservation law of the given system. The second formula checks a priori whether or not the action of a symmetry (continuous or discrete) on a conservation law can yield one or more new conservation laws of the given system. Several examples are considered, including the use of a discrete symmetry to obtain a new conservation law and the use of a continuous symmetry to generate two new conservation laws.     

Conservation laws for nonlinear telegraph equations

A complete conservation law classification is given for nonlinear telegraph (NLT) systems with respect to multipliers that are functions of independent and dependent variables. It turns out that a very large class of NLT systems admits four nontrivial local conservation laws. The results of this work are summarized in tables which display all multipliers, fluxes and densities for the corresponding conservation laws. A physical example is considered for possible applications.     

Quasiperiodic Solutions of the Heisenberg Ferromagnet Hierarchy

We present quasi-periodic solutions in terms of Riemann theta functions of the Heisenberg ferromagnet hierarchy by using algebro-geometric method. Our main tools include algebraic curve and Riemann surface, polynomial recursive formulation and a special meromorphic function.