The second variation formula for exponentially harmonic maps

Stable Exponentially Harmonic Maps Between Finsler Manifolds

stable exponentially harmonic maps between finsler manifolds

Energy of Harmonic Maps and Gardiner’s Formula

It is shown that the usual first variational formula for the energy of a harmonic map (or equivariant harmonic map) with respect to the conformal structure on a two dimensional domain extends to case of nonpositively curved metric space targets. As applications, we recover Gardiner’s formula for the variation of the Hubbard-Masur differential and a proof of the existence and uniqueness of quadr...

A Class of Exponentially Fitted Second Derivative Extended Backward Differentiation Formula for Solving Stiff Problems

An exponentially fitted second derivative extended backward differentiation formula (SDEBDF) is derived from the class of composite, multiderivative linear multistep method with a free parameter to allow for the exponential fitting. Some numerical properties such as stability of the methods are investigated as a pair of predictor-corrector (P-C) technique based on a proposed algorithm, to which...

Galerkin Finite-Element Method for the Analysis of the Second Harmonic Generation in Wagon Wheel Fibers

The nonlinear effects of the second harmonic generation have been investigated for the propagation of light along the axis of fibers of wagon wheel cross sectional shape. Nodal finite element formulation is utilized to obtain discretized Helmholtz equations under appropriate boundary conditions. The hierarchical p-version nodal elements are used for meshing the cross section of wagon wheel fibe...