A nonlinear fourth-order differential equation with arbitrary refractive index for description of the pulse propagation in an optical fiber is considered. The Cauchy problem for this equation cannot be solved by the inverse scattering transform and we look for solutions of the equation using the traveling wave reduction. We present a novel method for finding soliton solutions of nonlinear evolution equations. The essence of this method is based on the hypothesis about the possible type of an auxiliary equation with an already known solution. This new auxiliary equation is used as a basic equation to look for soliton solutions of the original equation. We have found three forms of soliton solutions of the equation at some constraints on parameters of the equation.

考虑用于描述光纤中脉冲传播的具有任意折射率的非线性四阶微分方程。该方程的柯西问题不能通过逆散射变换解决，我们使用行波减少法寻找方程的解。我们提出了一种寻找非线性发展方程孤子解的新方法。该方法的本质是基于关于具有已知解决方案的辅助方程的可能类型的假设。这个新的辅助方程式用作寻找原始方程式孤子解的基本方程式。我们发现了方程的孤子解的三种形式，它们对方程的参数有一些约束。