A global theory of internal solitary waves in two-fluid systems

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 g . It is assumed that a fluid of constant density ρ + {ρ _ + } lies above a fluid of constant density ρ − > ρ + > 0 {ρ _ - } > {ρ _ + } > 0 and that the system is nondiffusive. Progressing solitary waves, viewed in a moving coordinate system, can be described by a pair ( λ , w ) (λ ,w) , where the constant λ = g / c 2 λ = g/{c^2} , c c being the wave speed, and where w ( x , η ) + η w(x,η ) + η is the height at a horizontal position x x of the streamline which has height η η at x = ± ∞ x = ± ∞ . It is shown that among the nontrivial solutions of a quasilinear elliptic eigenvalue problem for ( λ , w )