## Abstract

A time domain method building on the concept of wave splitting is used to

study direct wave propagation phenomena in weakly nonlinear media. The

starting point is the linear wave equation with time-dependent coefficients.

This means that the studied nonlinear medium in some sense has to be approximated

with a nonstationary medium which changes while the wave passes

through. For the nonstationary equation homogeneous as well as particular

solutions can be obtained. Two different iterative procedures to find the nonlinear

solutions are discussed. They are illustrated by two problems fetched

from different research fields of current interest. In the first case, the nonlinear

term is linearized using the Fr´echet derivative. This leads into a truly

nonstationary, mixed initial boundary value problem with a linear equation

characterized by both time-dependent coefficients and source terms. In this

example a semiconductor device used for switching in high-frequency applications

is considered. It can be described as a coplanar waveguide loaded with

distributed resonant tunnel diodes. In the other example, wave propagation

in Kerr media is considered. Then Taylor expansion transforms the nonlinear

equation into a linear one with nonstationary source terms. In this case the

nonlinearity does not lead to time-depending coefficients in the equation. The

way to obtain the solution is a nonlinear variant of the Born approximation.

study direct wave propagation phenomena in weakly nonlinear media. The

starting point is the linear wave equation with time-dependent coefficients.

This means that the studied nonlinear medium in some sense has to be approximated

with a nonstationary medium which changes while the wave passes

through. For the nonstationary equation homogeneous as well as particular

solutions can be obtained. Two different iterative procedures to find the nonlinear

solutions are discussed. They are illustrated by two problems fetched

from different research fields of current interest. In the first case, the nonlinear

term is linearized using the Fr´echet derivative. This leads into a truly

nonstationary, mixed initial boundary value problem with a linear equation

characterized by both time-dependent coefficients and source terms. In this

example a semiconductor device used for switching in high-frequency applications

is considered. It can be described as a coplanar waveguide loaded with

distributed resonant tunnel diodes. In the other example, wave propagation

in Kerr media is considered. Then Taylor expansion transforms the nonlinear

equation into a linear one with nonstationary source terms. In this case the

nonlinearity does not lead to time-depending coefficients in the equation. The

way to obtain the solution is a nonlinear variant of the Born approximation.

Original language | English |
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Pages (from-to) | 185-235 |

Journal | Progress in Electromagnetics Research-Pier |

Volume | 17 |

DOIs | |

Publication status | Published - 1997 |

## Subject classification (UKÄ)

- Electrical Engineering, Electronic Engineering, Information Engineering
- Other Electrical Engineering, Electronic Engineering, Information Engineering