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The problem analyzed is that of two-dimensional wave motion in a heterogeneous, inviscid fluid confined between two rigid horizontal planes and subject to gravity g. It is assumed that a fluid of constant density p+ lies above a fluid of constant density p_ > p+ > 0 and that the system is nondiffusive. Progressing solitary waves, viewed in a moving coordinate system, can be described by a pair (A, w), where the constant A = g/c2, c being the wave speed, and where w(x, r¡) + r] is the height at a horizontal position x of the streamline which has height 77 at x = ±00. It is shown that among the nontrivial solutions of a quasilinear elliptic eigenvalue problem for (A, w) is an unbounded connected set in R x (Hq n C0,1). Various properties of the solution are shown, and the behavior of large amplitude solutions is analyzed, leading to the alternative that internal surges must occur or streamlines with vertical tangents must occur.

Progressing interfacial gravity waves are considered for two fluids of differing densities confined in a channel of finite vertical extent and infinite horizontal extent. An integrodifferential equation for the unknown shape of the interface is derived. This equation is discretized and the resulting algebraic equations are solved using Newton’s method. It is found that, for a range of heights and densities of the two fluids, the system supports a branch of solitary waves. Progression along the branch produces a broadening of the wave. With increased broadening both the amplitude and the wave speed approach limiting values. The results are in good agreement with analytical studies and indicate the existence of internal surges.