Results 91 to 100 of about 582,779 (212)

Darboux and binary Darboux transformations for discrete integrable systems I. Discrete potential KdV equation

, 2014
The Hirota–Miwa equation can be written in 'nonlinear' form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation.
Shi, Ying, Nimmo, Jonathan J C, Zhang, Da-jun   +2 more
core   +1 more source

Darboux-Moutard transformations and Poincare-Steklov operators [PDF]

, 2018
Formulas relating Poincare-Steklov operators for Schroedinger equations related by Darboux-Moutard transformations are derived. They can be used for testing algorithms of reconstruction of the potential from measurements at the boundary.Comment: 13 ...
Taimanov, I. A., Novikov, R. G., Novikov, Roman, Taimanov, Iskander   +3 more
core   +1 more source

B ̈acklund Transformations for Darboux Integrable Equations [PDF]

, 2011
Lie symmetry reduction is typically viewed as an integration method for differential systems of finite type, that is, systems of ordinary differential equations.
Anderson, Ian M.
core   +1 more source

Controlled excitation of multimodal soliton pulses in dispersion-decaying optical fibers [PDF]

AIP Advances
The investigation of mechanisms for the controlled excitation and modulation of localized optical field structures remains a pivotal theme in nonlinear optics.
Xiangshu Liu, Qicheng Chen, Xun Song, Yangmin Ou   +3 more
doaj   +1 more source

Darboux transformations of new supersymmetric CKP and BKP hierarchies

, 2017
In this paper, we construct a supersymmetric CKP(SCKP) hierarchy and its Darboux transformations. These Darboux transformations can generate new solutions from seed solutions by using supersymmetric functions.
Ruiling Ge, Chuanzhong Li
core   +1 more source

Vectorial Darboux Transformations for the Kadomtsev-Petviashvili Hierarchy [PDF]

, 1999
©Springer.We consider the vectorial approach to the binary Darboux transformations for the Kadomtsev-Petviashvili hierarchy in its Zakharov-Shabat formulation.
M. Mañas, Mañas Baena, Manuel Enrique, Liu, Q. P., Q. P. Liu   +3 more
core   +1 more source

Geometric Reinterpretation of Partial Differential Equations and Applications

Geometry
We 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
doaj   +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

On integrable reductions of two-dimensional Toda-type lattices

Partial Differential Equations in Applied Mathematics
The 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
doaj   +1 more source

Darboux transformations [PDF]

Transactions of the American Mathematical Society, 1967
Bruckner, A. M., Bruckner, J. B.
openaire   +1 more source