Stationary solitary, snoidal and sinusoidal ion acoustic waves

Stix's treatment of zero-damped electrostatic waves in a Maxwellian plasma is extended to the nonlinear regime. Stationary Bernstein-Greene-Krusk almodes which propagate with ion acoustic speed are constructed. This subclass consists of solitary, snoidal (=periodical waves, like ocean waves, which can be written in terms of Jacobian elliptic functions) and sinusoidal waves. A discrimination of those waves can be given by a single parameter, the steepness parameter, which contains nonlinearity, trapping of particles and dispersion. It turns out that Sadgeev's soliton represents a special case of the class solitons having the largest width and the lowest velocity. Hence a modified Korteweg-de-Vries equation must exist with a stronger nonlinearity.

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