Then,based on the wave theory,universal defining equation of composite radius-changing horn is given in exponential form,and the linear boundary condition is set to solve the sectionalized nonlinear equation to derive the general expressions of wave node position and amplification coefficient relevant to the horn.

On nonlinear differential equation with turning point involving two small parameters;

Quadratic integrability of solutions of a class of nonlinear differential equation;

The criterion of nonoscillation for nonlinear differential equation of second order;

Oscillation criteria for a kind of second-order nonlinear difference equation;

The existence of the positive solution to the second order nonlinear difference equation;

Permanence and global attractivity in nonlinear difference equation;

The entire gradual stability of a class of third order nonlinear differential equations;

A Study on Solving Nonlinear Differential Equations Using Accelerated Search-Extension Method and New Extrapolation Cascadic Multi-grid Method;

The Extension of the Theories about Liapunov s Concerning the Stability of Zero Solutions of Nonlinear Differential Equations and Its Applications;

In this paper,a sufficient and necessary condition to the linearization of one kind of one-order non-linear differential equation is given through the transformation of unknown-function,thus,the elementary solutions to a series of famous classic one-order non-linear differential equations are expanded.

In this paper, an algorithm for finding conservation laws of nonlinear difference equations is presented.

The existence of multiple periodic solutions is investigated for a class of second order non-autonomous nonlinear difference equations.

In this paper,we investigate the existence of multiple periodic solutions for a class of second order non-autonomous nonlinear difference equations with a parameter.