  Models for travelling waves in multi-fluid plasmas give essential insight
into fully nonlinear wave structures in plasmas, not readily available from
either numerical simulations or from weakly nonlinear wave theories. We
illustrate these ideas using one of the simplest models of an electron-proton
multi-fluid plasma for the case where there is no magnetic field or a constant
normal magnetic field present. We show that the travelling waves can be reduced
to a single first order differential equation governing the dynamics. We also
show that the equations admit a multi-symplectic Hamiltonian formulation in
which both the space and time variables can act as the evolution variable. An
integral equation useful for calculating adiabatic, electrostatic solitary wave
signatures for multi-fluid plasmas with arbitrary mass ratios is presented. The
integral equation arises naturally from a fluid dynamics approach for a two
fluid plasma, with a given mass ratio of the two species (e.g. the plasma could
be an electron proton or an electron positron plasma). Besides its intrinsic
interest, the integral equation solution provides a useful analytical test for
numerical codes that include a proton-electron mass ratio as a fundamental
constant, such as for particle in cell (PIC) codes. The integral equation is
used to delineate the physical characteristics of ion acoustic travelling waves
consisting of hot electron and cold proton fluids.
