Fully nonlinear traveling waves in multi-fluid plasmas have recently received considerable theoretical and observational attention in space plasma physics, as a consequence of progress in high time resolution satellite observations in the near Earth plasma environment by the FAST, Polar, Geotail and Cluster spacecraft. In this talk we present a dual (multi-symplectic) Hamiltonian description of traveling waves in a charge-neutral, electron-proton, non-relativistically moving plasma. The analysis is facilitated by using the de Hoffman-Teller (dHT) frame of MHD shock theory to simplify the transverse electron and proton momentum equations. We show that the governing equations are exactly integrable in the case where the total transverse momentum fluxes of the system are zero in the dHT frame. Numerical examples of integrable, oblique, traveling waves in a cold plasma are used to illustrate the physics. The transverse electron and proton velocity components exhibit complex rosette type patterns. The role of separatrices in the phase space, the rotational integral, and the longitudinal structure equation on the different wave forms are discussed.