Results 1 to 10 of about 2,221 (63)

Partial differential systems with non-local nonlinearities: generation and solutions. [PDF]

Philos Trans A Math Phys Eng Sci, 2018
We develop a method for generating solutions to large classes of evolutionary partial differential systems with nonlocal nonlinearities. For arbitrary initial data, the solutions are generated from the corresponding linearized equations.
Beck M, Doikou A, Malham SJA, Stylianidis I.   +3 more
europepmc   +4 more sources

The Cauchy problem for the Pavlov equation [PDF]

, 2014
Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs arising in various problems of mathematical physics and intensively studied in the recent literature.
Grinevich, P. G., Santini, P. M., Wu, D.
core   +1 more source

Riemann-Hilbert approach to multi-time processes; the Airy and the Pearcey case [PDF]

, 2011
We prove that matrix Fredholm determinants related to multi-time processes can be expressed in terms of determinants of integrable kernels \`a la Its-Izergin-Korepin-Slavnov (IIKS) and hence related to suitable Riemann-Hilbert problems, thus extending ...
Adler, Aptekarev, Bertola, Bertola, Bleher, Bleher, Bleher, Dyson, Harnad, Johansson, Johansson, M. Bertola, M. Cafasso, Okounkov, Prähofer, Simon, Soshnikov, Tracy, Tracy, Wang   +19 more
core   +4 more sources

Covariant constraints for generic massive gravity and analysis of its characteristics [PDF]

, 2014
We perform a covariant constraint analysis of massive gravity valid for its entire parameter space, demonstrating that the model generically propagates five degrees of freedom; this is also verified by a new and streamlined Hamiltonian description.
Deser, S., Sandora, M., Waldron, A., Zahariade, G.   +3 more
core   +3 more sources

The Generalized Dirichlet to Neumann map for the KdV equation on the half-line [PDF]

, 2006
For the two versions of the KdV equation on the positive half-line an initial-boundary value problem is well posed if one prescribes an initial condition plus either one boundary condition if $q_{t}$ and $q_{xxx}$ have the same sign (KdVI) or two ...
A. Boutet de Monvel, A. Boutet de Monvel, A. Boutet de Monvel, A. S. Fokas, A.S. Fokas, A.S. Fokas, A.S. Fokas, A.S. Fokas, A.S. Fokas, B. Engquist, C. Zheng, G.S. Gardner, J.E. Colliander, J.L. Bona, J.L. Bona, P. A. Treharne, P. Deift, P.D. Lax, V.E. Zakharov   +18 more
core   +1 more source

Numerical study of shock formation in the dispersionless Kadomtsev-Petviashvili equation and dispersive regularizations [PDF]

, 2013
The formation of singularities in solutions to the dispersionless Kadomtsev-Petviashvili (dKP) equation is studied numerically for different classes of initial data.
Klein, Christian, Roidot, Kristelle
core   +1 more source

Dressing method and quadratic bundles related to symmetric spaces. Vanishing boundary conditions [PDF]

, 2014
We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)x U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear Schroedinger ...
Valchev, Tihomir
core   +3 more sources

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
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Three-dimensional CFD simulations with large displacement of the geometries using a connectivity-change moving mesh approach [PDF]

, 2018
This paper deals with three-dimensional (3D) numerical simulations involving 3D moving geometries with large displacements on unstructured meshes. Such simulations are of great value to industry, but remain very time-consuming.
A Guardone, A Hay, A Loseille, A Loseille, AD Boer, B Koobus, B Nkonga, B Nkonga, C Debiez, C Degand, C Farhat, C Shu, CW Hirt, D Mavriplis, E Lefrançois, E Luke, F Alauzet, F Alauzet, F Alauzet, F Alauzet, Frédéric Alauzet, G Compere, G Sod, J Batina, J Bruchon, J Donea, JF Thompson, K Kitamura, L Chacón, L Formaggia, M Kucharik, M Lesoinne, N Barral, Nicolas Barral, O Hassan, P Batten, P Frey, P George, P Roe, PH Cournède, R Löhner, R Löhner, R Spiteri, S Etienne, T Baker, TJR Hughes, Z Yang   +46 more
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Cauchy Biorthogonal Polynomials

, 2009
The paper investigates the properties of certain biorthogonal polynomials appearing in a specific simultaneous Hermite-Pade' approximation scheme. Associated to any totally positive kernel and a pair of positive measures on the positive axis we define ...
Aptekarev, Aptekarev, Beals, Beals, Bertola, Bertola, Bertola, Bertola, Bertola, Bertola, Camassa, Cryer, Cryer, Degasperis, Duits, Ercolani, Eynard, Fidalgo Prieto, Gantmacher, J. Szmigielski, Jimbo, Karlin, Kuijlaars, Lundmark, Lundmark, M. Bertola, M. Gekhtman, Mehta, Nikishin, Nikišin, Sorokin, Sorokin, Sorokin, Van Assche   +33 more
core   +2 more sources