We present the method of group foliation for constructing non-invariant solutions of partial differential equations on an important example of the Boyer-Finley equation from the theory of gravitational instantons. We show that the commutativity con...
We reduce Boyer-Finley equation to a family of compatible systems of hydrodynamic type, with characteristic speeds expressed in terms of spaces of rational functions. The systems of hydrodynamic type are then solved by the generalized hodograph met...
High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML) (⭐ 624)
Vortons are closed loops of superconducting strings carrying current and charge. A formalism has been developed to study vortons in terms of an elastic string approximation, but its implementation requires knowledge of the unknown equation of state...
Butcher series appear when Runge-Kutta methods for ordinary differential equations are expanded in power series of the step size parameter. Each term in a Butcher series consists of a weighted elementary differential, and the set of all such differen...
Many sets of polarization evolution equations have been suggested to describe the method of polarization buildup by spin filtering in storage rings. In this paper a generic system of polarization evolution equations describing spin filtering is der...
Multiple (real) solutions of the CC equations (corresponding to the CCD, ACP and ACPQ methods) are studied for the PPP model of [10]annulene, C_{10}H_{10}. The long-range electrostatic interactions are represented either by the Mataga--Nishimoto po...
A simple counterexample against the Vlasov equation is put forward, in which a magnetized plasma is perturbed by an electromagnetic standing wave....
In this paper, we study the controllability of a Schrödinger equation with mixed boundary conditions on disjoint subsets of the boundary: dynamic boundary condition of Wentzell type, and Dirichlet boundary condition. The main result of this article...
In this paper we prove a uniform controllability result for a fourth order parabolic partial differential equation which includes a transport term, when the coefficients of higher order terms vanish. We prove the null controllability of the system wi...
In this paper, we investigate the analytical solutions of the compressible Navier-Stokes equations with dependent-density viscosity. By using the characteristic method, we successfully obtain a class of drifting solutions with elliptic symmetry for t...
We show in this work that every solution of hypoelliptic differential equations with constant strength with coefficients in Roumieu spaces is in some Roumieu space....
In this brief note we show that the author's previous result in \cite{cha} on the nonexistence of self-similar singularities for the 3D incompressible Euler equations implies actually the nonexistence of `locally self-similar' singular solution, wh...
Jan 31, 2014 · Help to clarify proof of Euler's Theorem on homogenous equations Ask Question Asked 12 years, 1 month ago Modified 1 year, 9 months ago
The role of the number of breakpoints $N$ in the sawtooth form of the characteristic function in the modified Chua's circuit model equation on vibrational and ghost-vibrational resonances is investigated in this paper. To observe vibrational resonanc...
We consider a family of conforming space-time finite element discretizations for the wave equation based on splines of maximal regularity in time. Traditional techniques may require a CFL condition to guarantee stability. Recent works by O. Steinbach...
We propose and analyze a space-time isogeometric finite element method based on splines with maximal regularity in time for the linear time-dependent Schrödinger equation with a spatially varying potential. We investigate the stability and conservat...
We extend the entropy stable high order nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations presented by Wintermeyer et al. [N. Wintermeyer, A. R. Winters, G. J. Gassner, and D. A. Ko...
We study entire solutions of the biharmonic heat equation on complete Riemannian manifolds without boundary. We provide exponential decay estimates for the biharmonic heat kernel under assumptions on the lower bound of Ricci curvature and noncollapsi...
We give a sufficient condition for global existence of the solutions to a generalized derivative nonlinear Schrödinger equation (gDNLS) by a variational argument. The variational argument is applicable to a cubic derivative nonlinear Schrödinger eq...