Results 31 to 40 of about 98,775 (107)

Darboux transformations for 5-point and 7-point self-adjoint schemes and an integrable discretization of the 2D Schrodinger operator

, 2003
With this paper we begin an investigation of difference schemes that possess Darboux transformations and can be regarded as natural discretizations of elliptic partial differential equations.
A. Doliwa, Ablowitz, Adler, Bogdanov, Doliwa, Doliwa, Doliwa, Dynnikov, Eisenhart, Ernst, Flaschka, Grundland, Hildebrand, Jonas, Konopelchenko, M. Nieszporski, Manakov, Manakov, Manas, Matveev, Misner, Moutard, Nieszporski, Nimmo, Novikov, Novikov, P.M. Santini, Schief, Shabat, Suris, Toda, Veselov   +31 more
core   +1 more source

Some Free Boundary Problems involving Nonlocal Diffusion and Aggregation

, 2015
We report on recent progress in the study of evolution processes involving degenerate parabolic equations what may exhibit free boundaries. The equations we have selected follow to recent trends in diffusion theory: considering anomalous diffusion with ...
Carrillo, Jose Antonio, Vazquez, Juan Luis   +1 more
core   +2 more sources

Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations

, 2016
We deal with a class of equations driven by nonlocal, possibly degenerate, integro-differential operators of differentiability order $s\in (0,1)$ and summability growth $p>1$, whose model is the fractional $p$-Laplacian with measurable coefficients.
Korvenpaa, Janne, Kuusi, Tuomo, Palatucci, Giampiero   +2 more
core   +1 more source

Partially integrable systems in multidimensions by a variant of the dressing method. 1

, 2006
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially integrable''.
A I Zenchuk, Ablowitz M J, Ablowitz M J, Beals R Coifman R R, Bogdanov L V, Calogero F, Drinfeld V G, Konopelchenko B, Manakov S V Santini P M, P M Santini, Zakharov V E, Zakharov V E, Zakharov V E, Zakharov V E, Zakharov V E, Zakharov V E, Zenchuk A   +16 more
core   +1 more source

Symbolic Computation of Conservation Laws of Nonlinear Partial Differential Equations in Multi-dimensions

, 2005
A direct method for the computation of polynomial conservation laws of polynomial systems of nonlinear partial differential equations (PDEs) in multi-dimensions is presented. The method avoids advanced differential-geometric tools.
Ablowitz, Ablowitz, Adams, Anco, Anco, Anderson, Anderson, Barnett, Cantarella, Deconinck, Dellar, Eklund, Faddeev, Gao, Gao, Göktaş, Göktaş, Hereman, Hereman, Hereman, Hickman, Krasil'shchik, Kruskal, Marsden, Newell, Olver, Sanz-Serna, Svendsen, Wolf, Wolf   +29 more
core   +1 more source

Nonlinearizing linear equations to integrable systems including new hierarchies with nonholonomic deformations

, 2009
We propose a scheme for nonlinearizing linear equations to generate integrable nonlinear systems of both the AKNS and the KN classes, based on the simple idea of dimensional analysis and detecting the building blocks of the Lax pair.
Kundu, Anjan
core   +1 more source

On nonlocal quasilinear equations and their local limits

, 2016
We introduce a new class of quasilinear nonlocal operators and study equations involving these operators. The operators are degenerate elliptic and may have arbitrary growth in the gradient.
Chasseigne, Emmanuel, Jakobsen, Espen
core   +1 more source

Semi analytical solution strategy for fractional Fornberg Whitham equation using Temimi Ansari method. [PDF]

Sci Rep
Arafa AAM, Elsaid EM, Ahmed SE, Hussein SA, Al Qarni AA, Eid MR.   +5 more
europepmc   +1 more source

Generative discovery of partial differential equations by learning from math handbooks. [PDF]

Nat Commun
Xu H, Chen Y, Cao R, Tang T, Du M, Li J, Callaghan AH, Zhang D.   +7 more
europepmc   +1 more source

Sharp Lyapunov inequalities and the emergence of chaos in discrete fractional systems. [PDF]

Sci Rep
Arab M, Mohammed PO, Baleanu D, Hamasalh FK.   +3 more
europepmc   +1 more source