Results 31 to 40 of about 8,283 (176)

Computing necessary integrability conditions for planar parametrized homogeneous potentials [PDF]

, 2014
Let $V\in\mathbb{Q}(i)(\a_1,\dots,\a_n)(\q_1,\q_2)$ be a rationally parametrized planar homogeneous potential of homogeneity degree $k\neq -2, 0, 2$. We design an algorithm that computes polynomial \emph{necessary} conditions on the parameters $(\a_1 ...
Bostan, Alin, Combot, Thierry, Mohab, Safey El Din   +2 more
core   +5 more sources

The Darboux transformation and algebraic deformations of shape-invariant potentials [PDF]

, 2003
We investigate the backward Darboux transformations (addition of a lowest bound state) of shape-invariant potentials on the line, and classify the subclass of algebraic deformations, those for which the potential and the bound states are simple ...
Gomez-Ullate, David, Kamran, Niky, Milson, Robert   +2 more
core   +3 more sources

Uniform treatment of Darboux’s method and the Heisenberg polynomials [PDF]

Proceedings of the American Mathematical Society, 2013
We show that the set of Heisenberg polynomials furnishes a simple non-trivial example in the uniform treatment of Darboux's method.
Liu, Sai-Yu, Wong, R., Zhao, Yu-Qiu
openaire   +3 more sources

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

From the Birkhoff-Gustavson normalization to the Bertrand-Darboux integrability condition

, 2000
The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the Birkhoff-Gustavson(BG)-normalization: By solving an inverse problem of the BG-normalization on computer algebra, it is
Arnold V I, Chekanov N A, Cushman R, Darboux G, Goldstein H, Grosche C, Kummer M, Moser J K, Perelomov A M, Spivak M, Uwano Y, Uwano Y, Uwano Y, Uwano Y, Uwano Y, Whittaker E T, Yamaguchi Y Y, Yoshio Uwano   +17 more
core   +2 more sources

The role of algebraic solutions in planar polynomial differential systems [PDF]

, 2005
We study a planar polynomial differential system, given by \dot{x}=P(x,y), \dot{y}=Q(x,y). We consider a function I(x,y)=\exp \{h_2(x) A_1(x,y) \diagup A_0(x,y) \} h_1(x) \prod_{i=1}^{\ell} (y-g_i(x))^{\alpha_i}, where g_i(x) are algebraic functions, A_1(
Giacomini, Héctor, Giné, Jaume, Grau, Maite   +2 more
core   +5 more sources

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

Closed Form Relations and Higher‐Order Approximations of First and Second Derivatives of the Tangent Operator on SE(3)

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 106, Issue 4, April 2026.
ABSTRACT The Lie group SE3$SE\left(3\right)$ of isometric orientation‐preserving transformation is used for modeling multibody systems, robots, and Cosserat continua. The use of these models in numerical simulation and optimization schemes necessitates the exponential map, its right‐trivialized differential (often referred to as the tangent operator ...
Andreas Müller
wiley   +1 more source

On the Darboux transformations and sequences of p-orthogonal polynomials [PDF]

Applied Mathematics and Computation, 2020
For a fixed $p \in \mathbb{N}$, sequences of polynomials $\{P_n\}$, $n \in \mathbb{N}$, defined by a $(p+2)$-term recurrence relation are related to several topics in Approximation Theory. A $(p+2)$-banded matrix $J$ determines the coefficients of the recurrence relation of any of such sequences of polynomials.
Barrios Rolanía, Maria Dolores, García Ardila, Juan Carlos, Manrique Gamo, Daniel   +2 more
openaire   +4 more sources

Local solutions to Darboux problem with a discontinuous right-hand side

Condensed Matter Physics, 2008
The existence of a local solution to the Darboux problem uxy(x,y)=g(u(x,y)), u(x,0)=u(0,y)=0, where g is Lebesgue measurable and has at most polynomial growth, is proved.
P.Pikuta
doaj   +1 more source