Results 21 to 30 of about 514 (43)

On the Galilean invariance of some dispersive wave equations [PDF]

, 2013
Surface water waves in ideal fluids have been typically modeled by asymptotic approximations of the full Euler equations. Some of these simplified models lose relevant properties of the full water wave problem. One of them is the Galilean symmetry, which
Abdulloev, Antonopoulos, Barthélémy, Benjamin, Benjamin, Bona, Bona, Bona, Bona, Bona, Boussinesq, Broer, Camassa, Carter, Chen, Chhay, Chhay, Christov, Clamond, Courtenay Lewis, Craig, Craik, de Saint-Venant, Degasperis, Dougalis, Dougalis, Dullin, Dutykh, Dutykh, Dutykh, Fenton, Fetecau, Gardner, Green, Green, Grimshaw, Johnson, Johnson, Kim, Kim, Korteweg, Lakoba, Lannes, Lax, Li, Li, Li, Longuet-Higgins, Luke, Miura, Nwogu, Olver, Pava, Pego, Pelinovsky, Peregrine, Peregrine, Petrov, Petviashvili, Salmon, Serre, Stoker, Su, Tanaka, Whitham, Yang, Zabusky, Zakharov   +67 more
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Adaptive meshless refinement schemes for RBF-PUM collocation

, 2018
In this paper we present an adaptive discretization technique for solving elliptic partial differential equations via a collocation radial basis function partition of unity method. In particular, we propose a new adaptive scheme based on the construction
Cavoretto, R., De Rossi, A.
core   +1 more source

PLANE WAVE STABILITY OF THE SPLIT-STEP FOURIER METHOD FOR THE NONLINEAR SCHRÖDINGER EQUATION

Forum of Mathematics, Sigma, 2014
Plane wave solutions to the cubic nonlinear Schrödinger equation on a torus have recently been shown to behave orbitally stable. Under generic perturbations of the initial data that are small in a high-order Sobolev norm, plane waves are stable over long
ERWAN FAOU, LUDWIG GAUCKLER, CHRISTIAN LUBICH   +2 more
doaj   +1 more source

The Initial Value Problem for Weakly Nonlinear PDE

, 2014
We will discuss an extension of the pseudospectral method developed by Wineberg, McGrath, Gabl, and Scott for the numerical integration of the KdV initial value problem.
Palais, Richard S.
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New, Highly Accurate Propagator for the Linear and Nonlinear Schr\"odinger Equation

, 2012
A propagation method for the time dependent Schr\"odinger equation was studied leading to a general scheme of solving ode type equations. Standard space discretization of time-dependent pde's usually results in system of ode's of the form u_t -Gu = s ...
A. Alvermanna, C. Leforestier, D. Kosloff, D.J. Tannor, H. Tal Ezer, H. Tal Ezer, H. Tal Ezer, H.-D. Meyer, Hillel Tal-Ezer, Ido Schaefer, J.P. Palao, M. Caliari, M. Hochbruck, M. Hochbruck, M. Hochbruck, M. Ndong, M. Ndong, M.D. Feit, N.J. Higham, Ronnie Kosloff, U. Peskin   +20 more
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Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor

, 2010
In this paper we provide a sufficient condition, in terms of only one of the nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity vector field, for the global regularity of strong solutions to the three-dimensional Navier-Stokes
C. Cao, C. Doering, C. He, Chongsheng Cao, D. Chae, Edriss S. Titi, G. Prodi, G. Raugel, G. Seregin, G.P. Galdi, H. Fujita, H. Sohr, H. Sohr, H.B. Da Veiga, I. Kukavica, I. Kukavica, J. Leray, J. Serrin, J.L. Lions, L. Escauriaza, L.C. Berselli, L.C. Berselli, M. Pokorný, M. Pokorný, O.A. Ladyzhenskaya, P. Constantin, P. Constantin, P.G. Lemarié–Rieusset, P.L. Lions, R. Sohr, R.A. Adams, T. Kato, Y. Giga, Y. Giga, Y. Zhou, Y. Zhou   +35 more
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The solution of the scalar wave equation in the exterior of a sphere

, 2013
We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions.
Greengard, Leslie, Hagstrom, Thomas, Jiang, Shidong   +2 more
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A new operational matrix based on Bernoulli polynomials [PDF]

, 2014
In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product.
Kazem, S., Parand, K., Rad, J. A., Shaban, M.   +3 more
core  

Pressure Regularity Criterion for the Three-dimensional Navier-Stokes Equations in Infinite Channel [PDF]

, 2007
In this paper we consider the three-dimensional Navier-Stokes equations in an infinite channel. We provide a sufficient condition, in terms of $\partial_z p$, where $p$ is the pressure, for the global existence of the strong solutions to the three ...
Cao, Chongsheng, Titi, Edriss S.
core   +1 more source

Accurate Simulation of Ideal Circular and Elliptic Cylindrical Invisibility Cloaks

, 2014
The coordinate transformation offers a remarkable way to design cloaks that can steer electromagnetic fields so as to prevent waves from penetrating into the {\em cloaked region} (denoted by $\Omega_0$, where the objects inside are invisible to observers
Wang, Li-Lian, Yang, Zhiguo
core   +1 more source