The nonlinear coupled system of diffusion equations are solved analytically for the transport and kinetics of electrons and reactant in the layer of a modified electrode. Analytical expressions of concentrations of su...The nonlinear coupled system of diffusion equations are solved analytically for the transport and kinetics of electrons and reactant in the layer of a modified electrode. Analytical expressions of concentrations of substrate and mediator are presented using He’s variational iteration method. The approximate expression of current for microheterogeneous catalysis at isonomer or redox polymer modified electrodes is also obtained. The results of the available limiting cases are compared with our results and are found to be in good agreement.展开更多
In this paper, by introducing a proper transformation, the （Gr/G）-expansion method is further extended into the nonlinear reaction diffusion equations in mathematical biology whose balancing numbers may be negative ...In this paper, by introducing a proper transformation, the （Gr/G）-expansion method is further extended into the nonlinear reaction diffusion equations in mathematical biology whose balancing numbers may be negative integer. As a result, hyperbolic function solutions and trigonometric function solutions with free parameters are obtained. When the parameters are taken as special values the solitary wave solutions and the periodic wave solutions are also derived from the traveling wave solutions. Moreover, it is observed that the suggested techniques is compatible of such problems.展开更多
In this paper, we consider a nonlinear system of reaction diffusion equa- tions arising from mathematical neuroscience and two nonlinear scalar reaction diffusion equations under some assumptions on their coefficients...In this paper, we consider a nonlinear system of reaction diffusion equa- tions arising from mathematical neuroscience and two nonlinear scalar reaction diffusion equations under some assumptions on their coefficients. The main purpose is to couple together linearized stability criterion （the equivalence of the nonlinear stability, the linear stability and the spectral sta- bility of the standing pulse solutions） and Evans functions to accomplish the existence and instability of standing pulse solutions of the nonlinear system of reaction diffusion equations and the nonlinear scalar reaction diffusion equa- tions. The Evans functions for the standing pulse solutions are constructed explicitly.展开更多
文摘The nonlinear coupled system of diffusion equations are solved analytically for the transport and kinetics of electrons and reactant in the layer of a modified electrode. Analytical expressions of concentrations of substrate and mediator are presented using He’s variational iteration method. The approximate expression of current for microheterogeneous catalysis at isonomer or redox polymer modified electrodes is also obtained. The results of the available limiting cases are compared with our results and are found to be in good agreement.
文摘In this paper, by introducing a proper transformation, the （Gr/G）-expansion method is further extended into the nonlinear reaction diffusion equations in mathematical biology whose balancing numbers may be negative integer. As a result, hyperbolic function solutions and trigonometric function solutions with free parameters are obtained. When the parameters are taken as special values the solitary wave solutions and the periodic wave solutions are also derived from the traveling wave solutions. Moreover, it is observed that the suggested techniques is compatible of such problems.
基金supported by a Faculty Research Grant of Lehigh University
文摘In this paper, we consider a nonlinear system of reaction diffusion equa- tions arising from mathematical neuroscience and two nonlinear scalar reaction diffusion equations under some assumptions on their coefficients. The main purpose is to couple together linearized stability criterion （the equivalence of the nonlinear stability, the linear stability and the spectral sta- bility of the standing pulse solutions） and Evans functions to accomplish the existence and instability of standing pulse solutions of the nonlinear system of reaction diffusion equations and the nonlinear scalar reaction diffusion equa- tions. The Evans functions for the standing pulse solutions are constructed explicitly.
