Symbolic Computation of Polynomial Conserved Densities, Generalized Symmetries, and Recursion Operators for Nonlinear Differential-Difference Equations [PDF]
, 2004 Algorithms for the symbolic computation of polynomial conserved densities, fluxes, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations are presented. In the algorithms we use discrete versions of the
Jan A. S +15 more
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A class of equations with peakon and pulson solutions (with an Appendix by Harry Braden and John Byatt-Smith) [PDF]
, 2005 We consider a family of integro-differential equations depending upon a parameter b as well as a symmetric integral kernel g(x). When b=2 and g is the peakon kernel (i.e.
N W Hone +3 more
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Hierarchical bases for non-hierarchic 3Dtriangular meshes [PDF]
, 2008 We describe a novel basis of hierarchical, multiscale functions that are linear combinations of standard Rao-Wilton- Glisson (RWG) functions. When the basis is used for discretizing the electric field integral equation (EFIE) for PEC objects it gives ...
Vecchi, Giuseppe +2 more
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High-Order Integral Equation Methods for Diffraction Problems Involving Screens and Apertures [PDF]
, 2012 This thesis presents a novel approach for the numerical solution of problems of diffraction by infinitely thin screens and apertures. The new methodology relies on combination of weighted versions of the classical operators associated with the Dirichlet ...
Lintner, Stéphane Karl
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Numerical methods for boundary value problems on random domains [PDF]
, 2014 In this thesis, we consider the numerical solution of elliptic boundary value problems on random domains. The underlying domain is modelled via a random vector field which is given by its mean and its covariance.
Peters, Michael
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Darboux transformation with dihedral reduction group [PDF]
, 2014 We construct the Darboux transformation with Dihedral reduction group for the 2-dimensional generalisation of the periodic Volterra lattice. The resulting Bäcklund transformation can be viewed as a nonevolutionary integrable differential difference ...
Papamikos, Georgios +6 more
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On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations [PDF]
, 2015 We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components.
Klein, Christian +13 more
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Spectral and scattering theory for ordinary differential equations
, 2020 This graduate textbook offers an introduction to the spectral theory of ordinary differential equations, focusing on Sturm–Liouville equations. Sturm–Liouville theory has applications in partial differential equations and mathematical physics.
Weikard, Rudi +2 more
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Multiscale expansion and integrability properties of the lattice potential KdV equation
, 2008 We apply the discrete multiscale expansion to the Lax pair and to the first few symmetries of the lattice potential Korteweg-de Vries equation. From these calculations we show that, like the lowest order secularity conditions give a nonlinear Schrödinger
Decio Levi +10 more
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Asymptotically Optimal High-Order Accurate Algorithms for the Solution of Certain Elliptic PDEs [PDF]
, 2008 The main goal of the project, "Asymptotically Optimal, High-Order Accurate Algorithms for the Solution of Certain Elliptic PDE's" (DE-FG02-03ER25577) was to develop fast, high-order algorithms for the solution of scattering problems and spectral problems
Kunyansky, Leonid
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