Sentence examples for using a perturbation principle from inspiring English sources

The restriction on distinctness of eigenvalues is removed in [2] (see also [6, 7] in the discrete case) using a perturbation principle, then Theorem 1 remains true when Krein's traffic rules for eigenvalues are preserved.

The velocity fields are obtained using a perturbation analysis.

An analytical solution for quadratic nonlinear wave-current interactions is derived using a perturbation method.

This result is arrived at using a perturbation analysis exactly as considered in the previous subsection.

We use a perturbation method around an equilibrium.

We use a perturbation approach to construct the solutions.

The rest of the method is to use a perturbation expansion (also known as Hirota perturbation) in a Hirota bilinear form, collect the coefficients of perturbation parameter and analyze the conditions for multi-soliton solutions.

We use a perturbation theory to quantify the coupling between oceanic and atmospheric waves.

One-term perturbation corrections for both cases are also obtained using a singular perturbation method.

Perturbations related to a cumulative output V are also investigated by using a multiplicative perturbation theorem of Desch and Schappacher.

The speed of the power flow algorithm has been improved using a simple perturbation technique.