Mathematical tricks for pseudopotentials in the theories of nonlinear waves in plasmas

In the analysis of nonlinear waves in plasma, especially for search periodic waves, shock and solitons, mechanical analogy methods are widely applicable. The most famous them is Sagdeev pseudopotential method. However, sometimes mathematical difficulties arise when deriving formulas pseudopotentials. author proposes three tricks to get around these obtain exact pseudopotentials cases where direct, method considered inapplicable: a trick based on Lambert W-function, inverse function integration, reducing theory equations Bernoulli differential equation (the method). This article, which methodological by nature, provides detailed examples application each