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以三阶克尔型非线性波导为例，利用雅可比椭圆函数的特性，定义了一种新颖的雅可比椭圆余切振幅函数，以此建立了类似线性的在非线性条件下的色散关系，使形式简化、物理意义清晰。并利用这一关系分析了该情况下的模式特性和场特性。
Taking a three - order Kerr - type nonlinear waveguide as an example, a novel Jacobian elliptical cotangent amplitude function is defined by using the properties of Jacobian elliptic function. The linearity of the dispersion relation under nonlinear conditions is established. Make the form simplified, the physical meaning is clear. And use this relationship to analyze the mode characteristics and field characteristics in this case.