We consider Levi non-degenerate tube hypersurfaces in Cn+1 that are (k, n−k)-spherical, i.e., locally CR-equivalent to the hyperquadric with Levi form of the signature (k, n − k), with n ≤ 2k. We show that the number of affine equivalence classes of such hypersurfaces is infinite (in fact, uncountable) in the following cases: (i) k = n − 2, n ≥ 7; (ii) k = n − 3, n ≥ 7; (iii) k ≤ n − 4. For all...

This paper treats a holomorphic self-mapping f : Ω → Ω of a bounded domain Ω in a separable Hilbert space H with a fixed point p. In case the domain is convex, we prove an infinitedimensional version of the Cartan-Carathéodory-Kaup-Wu Theorem. This is basically a rigidity result in the vein of the uniqueness part of the classical Schwarz lemma. The main technique, inspired by an old idea of H. ...

This work presents a derivation of the energy density and energy flux of surface waves modeled by the so-called Kaup system, a variant of the Boussinesq system. The derivation is based on reconstruction of the velocity field and the pressure in the fluid column below the free surface, and is an extension of a method recently proposed in [2]. In the present note, it is shown that the total energ...

Abstract The Landau-Ginzburg-Higgs (LGH) equation explains the ocean engineering models, superconductivity and drift cyclotron waves in radially inhomogeneous plasma for coherent ion-cyclotron waves. In this paper, with a simple modification of Ablowitz-Kaup-Newell-Segur (AKNS) formalism, integrability LGH is proved by deriving Lax pair. Hence that, inverse scattering transformation (IST) appli...

The connection between motion of space or plane curves and integrable equations has drawn wide interest in the past and many results have been obtained. The pioneering work is due to Hasimoto where he showed in [1] that the nonlinear Schrödinger equation describes the motion of an isolated non-stretching thin vortex filament. Lamb [2] used the Hasimoto transformation to connect other motions of...