Results 91 to 100 of about 11,987 (207)

Deformed solitons of a typical set of (2+1)–dimensional complex modified Korteweg–de Vries equations

International Journal of Applied Mathematics and Computer Science, 2020
Deformed soliton solutions are studied in a typical set of (2+1)-dimensional complex modified Korteweg–de Vries (cmKdV) equations. Through constructing the determinant form of the n-fold Darboux transformation for these (2+1)-dimensional cmKdV equations,
Yuan Feng, Zhu Xiaoming, Wang Yulei
doaj   +1 more source

Product of Exponentials (POE) Splines on Lie‐Groups: Limitations, Extensions, and Application to SO(3)$$ SO(3) $$ and SE(3)$$ SE(3) $$

International Journal for Numerical Methods in Engineering, Volume 126, Issue 14, 30 July 2025.
ABSTRACT Existing methods for constructing splines and Bézier curves on a Lie group G$$ G $$ involve repeated products of exponentials deduced from local geodesics, w.r.t. a Riemannian metric, or rely on general polynomials. Moreover, each of these local curves is supposed to start at the identity of G$$ G $$.
Andreas Müller
wiley   +1 more source

Discrete Darboux transformation for discrete polynomials of hypergeometric type

, 1998
Darboux Transformation, well known in second order differential operator theory, is applied here to the difference equation satisfied by the discrete hypergeometric polynomials(Charlier, Meixner-Krawchuk, Hahn)
, Askey R, Darboux G, Gaspard Bangerezako, Kalnins E G, Magnus A P, Magnus A P, Miller W Jr, Nikiforov A, Shabat A, Shabat A B, Smirnov Yu F, Spiridonov V, Spiridonov V, Spiridonov V   +14 more
core   +1 more source

Uncovering fine‐scale surface flow dynamics with particle tracking velocimetry: A new benchmark for soil erosion modelling

Earth Surface Processes and Landforms, Volume 50, Issue 9, Page 1-18, July 2025.
This study introduces a camera‐based approach for distributed, high‐resolution flow velocity measurements during artificial rainfall simulations, using particle tracking velocimetry (PTV). The results demonstrate PTV's potential as a robust and easily implementable tool for improving runoff model assessment and process understanding at small scales ...
Lea Epple, Anne Bienert, Oliver Grothum, Jonas Lenz, Anette Eltner   +4 more
wiley   +1 more source

Quasi-Grammian Solutions of the Generalized Coupled Dispersionless Integrable System

Symmetry, Integrability and Geometry: Methods and Applications, 2012
The standard binary Darboux transformation is investigated and is used to obtain quasi-Grammian multisoliton solutions of the generalized coupled dispersionless integrable system.
Bushra Haider, Mahmood-ul Hassan
doaj   +1 more source

Darboux transformation for classical acoustic spectral problem

International Journal of Mathematics and Mathematical Sciences, 2003
We study discrete isospectral symmetries for the classical acoustic spectral problem in spatial dimensions one and two by developing a Darboux (Moutard) transformation formalism for this problem.
A. A. Yurova, A. V. Yurov, M. Rudnev
doaj   +1 more source

Darboux Transformation of the Green Function for the Dirac Equation with the Generalized Potential

, 2007
We consider the Darboux transformation of the Green functions of the regular boundary problem of the one-dimensional stationary Dirac equation. We obtained the Green functions of the transformed Dirac equation with the initial regular boundary conditions.
Bagrov V. G., Darboux G., Darboux G., EKATERINA POZDEEVA, Pozdeeva E. O., Pupasov A. M., Song D.-Y., Witten E.   +7 more
core   +1 more source

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.
europepmc   +1 more source

Algebraic construction of the Darboux matrix revisited

, 2009
We present algebraic construction of Darboux matrices for 1+1-dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case.
Arnold W I, Bart H, Belinsky V A, Bobenko A I, Bobenko A I, Bohner M, Boiti M, Boutet de Monvel A, Burtsev S P, Cieśliński J, Cieśliński J L, Cieśliński J L, Cieśliński J L, Cieśliński J L, Coley A, Darboux G, Doktorov E V, Gohberg I, Gu G C, Gu G C, Guest M A, Hoenselaers C, Its A R, Jan L Cieśliński, Krichever I M, Leble S B, Levi D, Matveev V B, Mañas M, Meinel R, Mikhailov A V, Mikhailov A V, Neugebauer G, Nijhoff F, Nimmo J J C, Novikov S P, Oevel W, Pressley A N, Rogers C, Sakhnovich A L, Sakhnovich L A, Sakhnovich L A, Saleem U, Shabat A B, Shin H J, Terng C L, Uhlenbeck K, Zakharov V E, Zakharov V E, Zakharov V E, Zhou Z X   +50 more
core   +2 more sources

A new constrained mKP hierarchy and the generalized Darboux transformation for the mKP equation with self-consistent sources

, 2004
The mKP equation with self-consistent sources (mKPESCS) is treated in the framework of the constrained mKP hierarchy. We introduce a new constrained mKP hierarchy which may be viewed as the stationary hierarchy of the mKP hierarchy with self-consistent ...
Chen, Cheng, Cheng, Claude, Date, Deng, Dickey, Dickey, Doktorov, Estévez, Geng, Konopelchenko, Leon, Leon, Lin, Matveev, Mel’nikov, Mel’nikov, Mel’nikov, Mel’nikov, Mel’nikov, Mel’nikov, Oevel, Ohta, Sidorenko, Ting Xiao, Xiao, Ye, Yunbo Zeng, Zeng, Zeng, Zeng, Zeng   +32 more
core   +1 more source