Results 71 to 80 of about 2,288,345 (293)
Darboux transformation for two‐level system
Annalen der Physik, 2005 AbstractWe develop the Darboux procedure for the case of the two‐level system. In particular, it is demonstrated that one can construct the Darboux intertwining operator that does not violate the specific structure of the equations of the two‐level system, transforming only one real potential into another real potential.
Bagrov, V. +3 more
openaire +3 more sources
Large‐Amplitude Periodic Solutions to the Steady Euler Equations With Piecewise Constant Vorticity
Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.ABSTRACT We consider steady solutions to the incompressible Euler equations in a two‐dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation theory, we rigorously construct curves of solutions that terminate either with stagnation on the interface ...
Alex Doak +3 more
wiley +1 more source
Spectra of elliptic potentials and supersymmetric gauge theories
Journal of High Energy Physics, 2020 We study a relation between asymptotic spectra of the quantum mechanics problem with a four components elliptic function potential, the Darboux-Treibich-Verdier (DTV) potential, and the Omega background deformed N=2 supersymmetric SU(2) QCD models with ...
Wei He
doaj +1 more source
Self-Consistent Sources for Integrable Equations Via Deformations of Binary Darboux Transformations [PDF]
, 2015 We reveal the origin and structure of self-consistent source extensions of integrable equations from the perspective of binary Darboux transformations. They arise via a deformation of the potential that is central in this method.
O. Chvartatskyi +2 more
semanticscholar +1 more source
Exact solutions of the Gerdjikov-Ivanov equation using Darboux transformations [PDF]
Journal of Nonlinear Mathematical Physics, 2015 We study the Gerdjikov-Ivanov (GI) equation and present a standard Darboux transformation for it. The solution is given in terms of quasideterminants.
Halis Yilmaz
semanticscholar +1 more source
Bright and Dark Breathers on an Elliptic Wave in the Defocusing mKdV Equation
Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.ABSTRACT Breathers on an elliptic wave background consist of nonlinear superpositions of a soliton and a periodic wave, both traveling with different wave speeds and interacting periodically in the space‐time. For the defocusing modified Korteweg–de Vries equation, the construction of general breathers has been an open problem since the elliptic wave ...
Dmitry E. Pelinovsky, Rudi Weikard
wiley +1 more source
, 2009 This paper is concerned with a generalized type of Darboux transformations defined in terms of a twisted derivation $D$ satisfying $D(AB)=D(A)+\sigma(A)B$ where $\sigma$ is a homomorphism.
DeWitt B. +4 more
core +1 more source
A unified approach to Darboux transformations [PDF]
Inverse Problems, 2009 We analyze a certain class of integral equations related to Marchenko equations and Gel'fand-Levitan equations associated with various systems of ordinary differential operators. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution.
TUNCAY AKTOSUN +1 more
openaire +3 more sources
Exploring the Chavy–Waddy–Kolokolnikov Model: Analytical Study via Recently Developed Techniques
Journal of Mathematics, Volume 2026, Issue 1, 2026.This work explores the analytical soliton solutions to the Chavy–Waddy–Kolokolnikov equation (CWKE), which is a well‐known equation in biology that shows how light‐attracted bacteria move together. This equation is very useful for analyzing pattern creation, instability regimes, and minor changes in linear situations since bacterial movement is very ...
Jan Muhammad +3 more
wiley +1 more source
Spectral problem for the complex mKdV equation: singular manifold method and Lie symmetries [PDF]
Open Communications in Nonlinear Mathematical PhysicsThis article addresses the study of the complex version of the modified Korteweg-de Vries equation using two different approaches. Firstly, the singular manifold method is applied in order to obtain the associated spectral problem, binary Darboux ...
Paz Albares +3 more
doaj +1 more source