Results 71 to 80 of about 276 (182)
Darboux transformation for the discrete Schrödinger equation
Electronic Journal of Differential Equations, 2018 The discrete Schrödinger equation on a half-line lattice with the Dirichlet boundary condition is considered when the potential is real valued, is summable, and has a finite first moment. The Darboux transformation formulas are derived from first principles showing how the potential and the wavefunction change when a bound state is added to or removed ...
Tuncay Aktosun +2 more
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Controlled excitation of multimodal soliton pulses in dispersion-decaying optical fibers [PDF]
AIP AdvancesThe investigation of mechanisms for the controlled excitation and modulation of localized optical field structures remains a pivotal theme in nonlinear optics.
Xiangshu Liu +3 more
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Geometric Reinterpretation of Partial Differential Equations and Applications
GeometryWe obtain improved regularity estimates on solutions of partial differential equations by combining the method of Fuchsian Reduction with geometric transformations. Examples include the meron problem and the regularity of the conformal radius.
Satyanad Kichenassamy
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On integrable reductions of two-dimensional Toda-type lattices
Partial Differential Equations in Applied MathematicsThe article considers lattices of the two-dimensional Toda type, which can be interpreted as dressing chains for spatially two-dimensional generalizations of equations of the nonlinear Schrödinger type.
I.T. Habibullin, A.U. Sakieva
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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.
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Symmetry, Integrability and Geometry: Methods and Applications, 2013 We present a general solution-generating result within the bidifferential calculus approach to integrable partial differential and difference equations, based on a binary Darboux-type transformation.
Aristophanes Dimakis +1 more
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Transactions of the American Mathematical Society, 1967 Bruckner, A. M., Bruckner, J. B.
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Results in PhysicsNonlinear wave phenomena have attracted considerable attention since the discovery of solitons by Zabusky and Kruskal. These phenomena play an important role in various areas of science and are described by nonlinear partial differential equations. Among
Meruyert Zhassybayeva +3 more
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The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 1 [PDF]
Opuscula Mathematica, 2006 The structure properties of multidimensional Delsarte-Darboux transmutation operators in parametric functional spaces are studied by means of differential-geometric and topological tools.
Yarema A. Prykarpatsky +1 more
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Symmetry, Integrability and Geometry: Methods and Applications, 2013 Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation.
Kenichi Kondo
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