Results 61 to 70 of about 11,987 (207)

Darboux transformation and solution of the modified Korteweg–de Vries equation

Қарағанды университетінің хабаршысы. Математика сериясы, 2015
Darboux transformation and a comprehensive approach to construct exact solutions of the nonlinear differential equation are counted. It is applied to construct the explicit solutions of the (2+1)-dimensional modified Korteweg-de Vries (KdV) equation. In
G. Kemelbekova, K. Yesmakhanova, S. Tapeeva, D. Tungushbaeva   +3 more
doaj  

Two binary Darboux transformations for the KdV hierarchy with self-consistent sources

, 2001
Two binary (integral type) Darboux transformations for the KdV hierarchy with self-consistent sources are proposed. In contrast with the Darboux transformation for the KdV hierarchy, one of the two binary Darboux transformations provides non auto-B\"{a ...
Antonowicz, Chen, Claude, Doktorov, Doktorov, Kaup, Leon, Leon, Leon, Ma, Ma, Mel’nikov, Mel’nikov, Mel’nikov, Mel’nikov, Mel’nikov, Mel’nikov, Nakazawa, Shchesnovich, Vlasov, Wen-Xiu Ma, Yijun Shao, Yu Orlov, Yunbo Zeng, Zakharov, Zeng, Zeng, Zeng, Zeng, Zeng, Zeng   +30 more
core   +2 more sources

A Discrete Mechanics Approach to the Cosserat Rod Theory—Part II: Geometric Insights About Static Equilibria on Vertex and Staggered Grids

International Journal for Numerical Methods in Engineering, Volume 126, Issue 23, 15 December 2025.
ABSTRACT We apply the discrete mechanics approach to the discretisation of geometrically exact Cosserat rods. We consider discrete Cosserat rods defined on a vertex (or nodal) grid, as well as on a staggered grid, and provide a review and update of the results already obtained in Part I for the nodal model variant and, for the first time, present a ...
Holger Lang, Rodrigo T. Sato Martín de Almagro, Tengman Wang, Martina Stavole, Joachim Linn, Sigrid Leyendecker   +5 more
wiley   +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, VAN DER MEE, CORNELIS VICTOR MARIA   +1 more
openaire   +3 more sources

A Five-Component Generalized mKdV Equation and Its Exact Solutions

Mathematics, 2020
In this paper, a 3 × 3 spectral problem is proposed and a five-component equation that consists of two different mKdV equations is derived. A Darboux transformation of the five-component equation is presented relating to the gauge transformations
Bo Xue, Huiling Du, Ruomeng Li
doaj   +1 more source

Numerical and Analytical Investigation of the Ablowitz–Ladik and Salerno Models: Closeness to Cubic and Cubic‐Quintic Discrete Nonlinear Schrödinger Lattices

Studies in Applied Mathematics, Volume 155, Issue 6, December 2025.
ABSTRACT We study the closeness between the Ablowitz–Ladik, Salerno, and discrete nonlinear Schrödinger lattices in regimes of small coupling ε$\varepsilon$ and small energy norm ρ$\rho$. Two approaches are compared: direct estimates in physical variables and a transformation to canonical symplectic coordinates via Darboux variables.
Marco Calabrese, Tiziano Penati, Simone Paleari   +2 more
wiley   +1 more source

Darboux-type transformations and hyperelliptic curves [PDF]

Journal für die reine und angewandte Mathematik (Crelles Journal), 2000
We systematically study Darboux-type transformations for the KdV and AKNS hierarchies and provide a complete account of their effects on hyperelliptic curves associated with algebro-geometric solutions of these hierarchies.
Gesztesy, Fritz, Holden, Helge
openaire   +3 more sources

Floer theory for the variation operator of an isolated singularity

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract The variation operator in singularity theory maps relative homology cycles to compact cycles in the Milnor fiber using the monodromy. We construct its symplectic analog for an isolated singularity. We define the monodromy Lagrangian Floer cohomology, which provides categorifications of the standard theorems on the variation operator and the ...
Hanwool Bae, Cheol‐Hyun Cho, Dongwook Choa, Wonbo Jeong   +3 more
wiley   +1 more source

A Method for Obtaining Darboux Transformations [PDF]

Journal of Nonlinear Mathematical Physics, 1998
In this paper we give a method to obtain Darboux transformations (DTs) of integrable equations. As an example we give a DT of the dispersive water wave equation. Using the Miura map, we also obtain the DT of the Jaulent-Miodek equation. \end{abstract}
Lu, Baoqun, He, Yong, Ni, Guangjiong
openaire   +2 more sources

Soliton Solutions for the Wick-Type Stochastic KP Equation

Abstract and Applied Analysis, 2012
The Wick-type stochastic KP equation is researched. The stochastic single-soliton solutions and stochastic multisoliton solutions are shown by using the Hermite transform and Darboux transformation.
Y. F. Guo, L. M. Ling, D. L. Li
doaj   +1 more source