Results 91 to 100 of about 9,686 (209)
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
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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
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
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
Earth Surface Processes and Landforms, Volume 50, Issue 9, Page 1-18, July 2025.This study introduces a camera‐based approach for distributed, high‐resolution flow velocity measurements during artificial rainfall simulations, using particle tracking velocimetry (PTV). The results demonstrate PTV's potential as a robust and easily implementable tool for improving runoff model assessment and process understanding at small scales ...
Lea Epple +4 more
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
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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.
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Wronskian-type determinant solutions of the nonlocal derivative nonlinear Schrödinger equation
AIMS MathematicsA nonlocal derivative nonlinear Schrödinger (DNLS) equation is analytically studied in this paper. By constructing Darboux transformations (DTs) of arbitrary order, new determinant solutions of the nonlocal DNLS equation in the form of Wronskian-type are
Dexin Meng
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