Results 111 to 120 of about 2,294,985 (248)
A note about isothermic surfaces in Rn-j,j
Revista Integración, 2008 In this note we survey our results on the description of ti- melike isothermic surfaces in Rn−j,j using the Grassmannian systems or U/K-systems. We give the natural extensions of the definition of Ribaucour and Darboux transformations for timelike ...
M. P. Dussan, M. A. Magid
doaj
Spectral curve, Darboux coordinates and Hamiltonian structure of periodic dressing chains
, 2002 A chain of one-dimensional Schr\"odinger operators connected by successive Darboux transformations is called the ``Darboux chain'' or ``dressing chain''. The periodic dressing chain with period $N$ has a control parameter $\alpha$.
Adams +21 more
core +4 more sources
Discrete Integrable Principal Chiral Field Model and Its Involutive Reduction
Studies in Applied Mathematics, Volume 155, Issue 2, August 2025.ABSTRACT We discuss an integrable discretization of the principal chiral field models equations and its involutive reduction. We present a Darboux transformation and general construction of soliton solutions for these discrete equations.
J. L. Cieśliński +3 more
wiley +1 more source
A note about isothermic surfaces in Rn−j,j
Revista Integración, 2009 In this note we survey our results on the description of ti-melike isothermic surfaces in Rn-j,j using the Grassmannian systems or U/K-systems. We give the natural extensions of the definition of Ribaucour and Darboux transformations for timelike ...
M P Dussan, M A Magid
doaj
High Order Solutions and Generalized Darboux Transformations of Derivative Schr\"odinger Equation
, 2012 By means of certain limit technique, two kinds of generalized Darboux transformations are constructed for the derivative nonlinear Sch\"odinger equation (DNLS).
Akhmdiev +25 more
core +1 more source
International Journal for Numerical Methods in Engineering, Volume 126, Issue 14, 30 July 2025.ABSTRACT Existing methods for constructing splines and Bézier curves on a Lie group G$$ G $$ involve repeated products of exponentials deduced from local geodesics, w.r.t. a Riemannian metric, or rely on general polynomials. Moreover, each of these local curves is supposed to start at the identity of G$$ G $$.
Andreas Müller
wiley +1 more source
Exact Propagators for Soliton Potentials
Symmetry, Integrability and Geometry: Methods and Applications, 2005 Using the method of Darboux transformations (or equivalently supersymmetric quantum mechanics) we obtain an explicit expression for the propagator for the one-dimensional Schrödinger equation with a multi-soliton potential.
Andrey M. Pupasov, Boris F. Samsonov
doaj
Separation of Coupled Systems of Schrodinger Equations by Darboux transformations
, 2011 Darboux transformations in one independent variable have found numerous applications in various field of mathematics and physics. In this paper we show that the extension of these transformations to two dimensions can be used to decouple systems of ...
Magri F. +3 more
core +1 more source
Integral transformation and Darboux transformation
, 2009 We review Darboux-Crum transformation of Heun's differential equation. By rewriting an integral transformation of Heun's differential equation into a form of elliptic functions, we see that the integral representation is a generalization of Darboux-Crum transformation. We also consider conservation of monodromy with respect to the transformations.
openaire +2 more sources
Transactions of the American Mathematical Society, 1967 Bruckner, A. M., Bruckner, J. B.
openaire +1 more source