Results 51 to 60 of about 8,235 (175)

The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2 [PDF]

Opuscula Mathematica, 2004
The structure properties of multidimensional Delsarte transmutation operators in parametric functional spaces are studied by means of differential-geometric tools.
J. Golenia, Y. A. Prykarpatsky, A. M. Samoilenko, A. K. Prykarpatsky   +3 more
doaj  

Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom

, 2009
We consider natural complex Hamiltonian systems with $n$ degrees of freedom given by a Hamiltonian function which is a sum of the standard kinetic energy and a homogeneous polynomial potential $V$ of degree $k>2$.
A. Guillot, A. J. Maciejewski, A. J. Maciejewski, A. K. Tsikh, A. Koz’owski, D. Cox, D. Cox, G. Biernat, G. Biernat, G. Biernat, H. A. Schwarz, H. Yoshida, H. Yoshida, I.A. Aĭzenberg, I.R. Shafarevich, J. Hietarinta, J. Hietarinta, J. J. Morales Ruiz, J. J. Morales Ruiz, J. J. Morales Ruiz, J. J. Morales Ruiz, J. J. Morales Ruiz, J. J. Morales Ruiz, K. Nakagawa, M. Audin, M. Przybylska, M. Przybylska, M.A. Almeida, P. Griffiths, P.A. Griffiths, P.F. Baum, S. L. Ziglin, S. L. Ziglin, T. Kimura   +33 more
core   +2 more sources

Krein-Adler transformations for shape-invariant potentials and pseudo virtual states [PDF]

, 2013
For eleven examples of one-dimensional quantum mechanics with shape-invariant potentials, the Darboux-Crum transformations in terms of multiple pseudo virtual state wavefunctions are shown to be equivalent to Krein-Adler transformations deleting multiple
Odake, Satoru, Sasaki, Ryu
core   +2 more sources

Exceptional Askey–Wilson-type polynomials through Darboux–Crum transformations [PDF]

Journal of Physics A: Mathematical and Theoretical, 2010
An alternative derivation is presented of the infinitely many exceptional Wilson and Askey-Wilson polynomials, which were introduced by the present authors in 2009. Darboux-Crum transformations intertwining the discrete quantum mechanical systems of the original and the exceptional polynomials play an important role.
Odake, Satoru, Sasaki, Ryu
openaire   +2 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, Karsten Matthies, Jonathan Sewell, Miles H. Wheeler   +3 more
wiley   +1 more source

Finiteness of integrable $n$-dimensional homogeneous polynomial potentials

, 2007
We consider natural Hamiltonian systems of $n>1$ degrees of freedom with polynomial homogeneous potentials of degree $k$. We show that under a genericity assumption, for a fixed $k$, at most only a finite number of such systems is integrable.
Ablowitz, Ablowitz, Furta, Goriely, Grammaticos, Grammaticos, Guillot, Hietarinta, Hietarinta, Iwasaki, Kowalevski, Kowalevski, Kozlov, Lakshmanan, Lyapunov, Maciejewski, Maciejewski, Maciejewski, Maria Przybylska, Morales-Ruiz, Morales-Ruiz, Morales-Ruiz, Nakagawa, Nowicki, Painlevé, Ramani, Ramani, van der Put, Whittaker, Yoshida, Yoshida, Ziglin, Ziglin   +32 more
core   +2 more sources

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

Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations [PDF]

Journal of Sciences, Islamic Republic of Iran, 2006
We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i.
doaj  

Askey-Wilson Type Functions, With Bound States

, 2003
The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it transparent that these functions satisfy a beautiful ...
A. Kasman, A.S. Zhedanov, B. Bakalov, B. Bakalov, D. Mumford, E. Koelink, F.A. Grünbaum, F.A. Grünbaum, F.A. Grünbaum, F.A. Grünbaum, F.W. Nijhoff, G. Andrews, G. Segal, G. Wilson, G. Wilson, H.L. Krall, I. Cherednik, J. Koekoek, J.J. Duistermaat, L. Haine, L. Haine, L. Haine, L.L. Littlejohn, Luc Haine, M. Rahman, M. Rahman, M. Toda, M.E.H. Ismail, P. Iliev, P. Iliev, Plamen Iliev, S. Bochner, S.K. Suslov, S.K. Suslov, T.H. Koornwinder, V.P. Spiridonov, W.N. Everitt   +36 more
core   +1 more source

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, David Yaro, Usman Younas, Chang Phang   +3 more
wiley   +1 more source