修正的Kortewey-de Vries方程的孤子解

利用一维波动方程的解具有行波解形式的特解的特点,给出行波解的形式.通过变量替换,再引入双曲正切函数作为独立变量,并利用双曲正切函数其独特的微分特性,给出1组变换,将修正的Kortewey-deVries方程简化为常微分方程,由此得出它的解.此解可作为物理学中非线性方程的实例.尽管不是所有的非线性波动方程都可以用此法来处理,但它缩短了线性和非线性波动理论之间的距离.

Soliton Solution of Rectified Kortewey-de Vries Equation

A traveling wave solution form is given by use of the characteristic that one dimentional undulant equation has traveling wave solution.A series of alternation is given,rectified Kortewey-de Vries equation be simplified into ordinary infinitesimal equation and its solution is obtained by alternation,introducing hypertangent as independent variable and making use of its infinitesimal connection.The solution can be considered as a instance of nonlinear equation in physics.The difference of linear undulant theory and nonlinear undulant theory can be reduced by using the method,but it isn't fit for all of nonlinear equations.