On One Widely-Spread Inaccuracy and Its Elimination in the Theories of Nonlinear Electrostatic Waves in Plasma Based on the Sagdeev’s Pseudopotential Approach

We report on the discovery of a contradiction appearing in the solutions to the problems of profiles of the nonlinear longitudinal electrostatic waves in plasma obtained using the Sagdeev’s pseudopotential approach. The contradiction reveals itself in the average over period particle concentration and given concentration of the unperturbed plasma being unequal to each other. It is demonstrated that the reason for the appearance of this contradiction is related to the relatively widely spread inaccuracy in the formulation of such problems. It is suggested correcting the formulation of such problems and changing interpretation of solutions obtained using the approach under consideration by imposing different initial conditions: it is necessary specifying particle concentration at the points where potential φ is set equal to zero instead of concentration of the unperturbed plasma. The contradiction is resolved completely when using such initial conditions.