Showing papers by "Wolfgang K. Schief published in 1997"
TL;DR: In this paper, a discrete analogue of the Moutard transformation is constructed by means of discrete analogues of the kink solutions of the continuous system, and it is shown that, in a particular form, this system is an integrable discretization of a (2+1)-dimensional sine-Gordon system.
Abstract: Superposition principles, both linear and nonlinear, associated with the Moutard transformation are found. On suitable reinterpretation, these constitute an integrable discrete nonlinear system and its associated linear system. Further, it is shown that, in a particular form, this system is an integrable discretization of a (2+1)–dimensional sine–Gordon system. Solutions of the discrete nonlinear system are constructed by means of a discrete analogue of the Moutard transformation. Included in these solutions are discrete analogues of the kink solutions of the continuous system.
133 citations
TL;DR: In this paper, the Darboux9s method of linking the classical Lame system governing triply orthogonal systems of surfaces with an integrable (2+1) -dimensional sine-Gordon equation was extended and applied to the integrably two-component generalization of the latter introduced by Konopelchenko and Rogers.
Abstract: It is recorded that Darboux9s method of linking the classical Lame system governing triply orthogonal systems of surfaces with an integrable (2+1)–dimensional sine–Gordon equation may be extended and applied to the integrable two–component generalization of the latter introduced by Konopelchenko and Rogers. Thus, in a reinterpretation, this (2+1)–dimensional sine–Gordon system is shown to define particular (integrable) motions of surfaces.
48 citations
TL;DR: In this paper, a Lie group approach is adopted to construct generalized Pinney equations of two distinct types which admit nonlinear superposition principles, and the procedure also provides a route to discretizations of these Pinney equation which preserves the property of admittance of a non linear superposition principle, and underlying linearizations are placed in the context of results for C-integrable nonlinear Schrodinger equations.
40 citations
TL;DR: In this paper, a system of two equations governing the irrotational flow of a capillary fluid is shown, for a particular class of free energy functions, to reduce to a nonlinear Schrodinger equation.
Abstract: A system of two equations governing the irrotational flow of a capillary fluid is shown, for a particular class of free energy functions, to reduce to a nonlinear Schrodinger equation.
33 citations
TL;DR: The general solution of the discrete Pinney equation is given in terms of two linearly independent solutions of a discrete Schrodinger equation.
31 citations
TL;DR: In this paper, a 1 + 1-dimensional non-linear equation descriptive of the dynamical deformation of a particular class of model nonlinear inhomogeneous media is linked to the geometry of pseudospherical surfaces.
13 citations
01 Jan 1997
TL;DR: In this article, the invariance under Laplace-Darboux-type transformations is established for the 2+1-dimensional Loewner-Konopelchenko-Rogers integrable system.
Abstract: Invariance under Laplace-Darboux-type transformations is established for the 2+1-dimensional Loewner-Konopelchenko-Rogers integrable system. This is exploited to derive a chain of novel, integrable Ernst-type equations which contain an arbitrary parameter.
7 citations