Perturbation method for a nonlinear wave modulation. III

Abstract

The perturbation method for the nonlinear, slow modulation of a rapidly oscillatory plane wave, which was given in the first paper of this series for a class of systems of nonlinear partial differential equations, is now established for a general system of nonlinear integro-partial differential equations. It is shown that the system can be reduced to simpler nonlinear equations which in certain cases become the nonlinear Schrödinger equation. The reduction proceeds as in the first paper, and the result is then applied to nonlinear optics.

Оптические Двухфотонные Поверхностные Нелинейные Волны

“…Для дальнейшего преобразования уравнения (5) при условии ≪ 1 можно воспользоваться пертурбативным методом редукции [22], согласно которому функция…”

Акустические Векторные Солитоны В Анизотропных Средах

“…Для анализа этих уравнений воспользуемся пертурбативным мето-дом редукции [4,11], согласно которому функцию…”

Soliton Propagation in Nonlinear Magnetic Metamaterials with Microscopic Disorder

“…Next, to investigate modulation of the linear solution FðÈ; Þ (2.16) due to the nonlinearities of the capacitance, we apply reductive perturbation analysis [32][33][34] to eq. (2.10) for R ¼ 0.…”

“…(2.10) for voltage, we obtain the linear solution (2.16) with (2.17), (2.23), and (2.24). Then, to examine the nonlinear modulation of the linear solution (2.16), we apply reductive perturbation analysis [32][33][34] to eq. (2.10).…”

“…This paper is organized as follows. In §2, by applying reductive perturbation analysis [32][33][34] to the time evolution equation for voltages across the SRRs' slits, we derive the nonlinear Schrödinger (NLS) equation with a stochastic term. In §3, we examine the deformation of solitons caused by randomness, such as the broadening of pulse width and the damping of amplitude.…”