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Integrability of Reeb Distribution Associated to a Generalized Engel Manifold
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this paper, we define a generalized Reeb distribution of an Engel 4n‐manifold and give a necessary and sufficient condition for integrability of this Reeb distribution which gives a generalization of some results of N. Pia about Reeb distributions of Engel 4‐manifolds.
Serigne Abdoul Aziz Dramé +3 more
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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
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APPLICATION OF DARBOUX TRANSFORMATION TO MULTIDIMENSIONAL INHOMOGENEOUS PROBLEMS
TASK Quarterly, 2016 General properties of ladder operators applied to inhomogeneous problems are studied in the context of their usefulness for solving practical problems with stress put on the possibility of embedding the interwine relation onto a wider class of operators.
GRZEGORZ KWIATKOWSKI
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Soliton solution, breather solution and rational wave solution for a generalized nonlinear Schrödinger equation with Darboux transformation. [PDF]
Sci Rep, 2023 Fan C, Li L, Yu F.
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Darboux Transformation for the 3-Dimension Nonlinear Schrodinger Equation
IEEE Photonics Journal, 2018 The transient nonlinear Schrodinger equation (NLSE) is solved with the Darboux transformation. Based on this solution, the longitude and transverse field evolution is presented; the time-varying coefficients (dispersion and nonlinear parameters) of NLSE ...
Mingxiang Gui, Jing Huang
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Darboux soft hair in 3D asymptotically flat spacetimes
Physics Letters BIn this paper, we construct a fully on-shell solution space for three-dimensional Einstein's gravity in asymptotically flat spacetimes using a finite coordinate transformation.
Vahid Taghiloo
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A new (1+1)-dimensional matrix k-constrained KP hierarchy [PDF]
Математичні Студії, 2013 We introduce a new generalization of matrix (1+1)-dimensional$k$-constrained KP hierarchy. The new hierarchy contains matrixgeneralizations of stationary DS systems, (2+1)-dimensionalmodified Korteweg-de Vries equation and the Nizhnik equation.
Yu. M. Sydorenko, O. I. Chvartatskyi
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AxiomsThe paper reveals some remarkable form-invariance features of the ‘Jacobi-reference’ canonical Sturm–Liouville equation (CSLE) in the particular case of the density function with the simple pole at the origin.
Gregory Natanson
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MathematicsThis paper conducts an in-depth study on the self-similar transformation, Darboux transformation, and the excitation and propagation characteristics of high-order bright–dark rogue wave solutions in the (2+1)-dimensional variable-coefficient Zakharov ...
Hangwei Zhang +3 more
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Restricted Flows and the Soliton Equation with Self-Consistent Sources
Symmetry, Integrability and Geometry: Methods and Applications, 2006 The KdV equation is used as an example to illustrate the relation between the restricted flows and the soliton equation with self-consistent sources. Inspired by the results on the Bäcklund transformation for the restricted flows (by V.B. Kuznetsov et al.
Runliang Lin, Haishen Yao, Yunbo Zeng
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