Abstract
In this paper, the focus is on numerical results from calculations of scattered
direct waves, originating from internal sources in non-stationary, dispersive,
stratified media. The mathematical starting point is a general, inhomogeneous,
linear, first order, 2 × 2 system of equations. Particular solutions
are obtained, as integrals of waves from point sources distributed inside the
scattering medium. Resolvent kernels are used to construct time dependent
fundamental wave functions at the location of the point source. Wave propagators,
closely related to the Green functions, at all times advance these
waves into the surrounding medium. Two illustrative examples are given.
First waves, propagating from internal sources in a Klein-Gordon slab, are
calculated with the new method. These wave solutions are compared to alternative
solutions, which can be obtained from analytical fundamental waves,
solving the Klein-Gordon equation in an infinite medium. It is shown, how
the Klein-Gordon wave splitting, which transforms the Klein-Gordon equation
into a set of uncoupled first order equations, can be used to adapt the infi-
nite Klein-Gordon solutions to the boundary conditions of the Klein-Gordon
slab. The second example hints at the extensive possibilities offered by the
new method. The current and voltage waves, evoked on the power line after
an imagined strike of lightning, are studied. The non-stationary properties
are modeled by the shunt conductance, which grows exponentially in time,
together with dispersion in the shunt capacitance.
direct waves, originating from internal sources in non-stationary, dispersive,
stratified media. The mathematical starting point is a general, inhomogeneous,
linear, first order, 2 × 2 system of equations. Particular solutions
are obtained, as integrals of waves from point sources distributed inside the
scattering medium. Resolvent kernels are used to construct time dependent
fundamental wave functions at the location of the point source. Wave propagators,
closely related to the Green functions, at all times advance these
waves into the surrounding medium. Two illustrative examples are given.
First waves, propagating from internal sources in a Klein-Gordon slab, are
calculated with the new method. These wave solutions are compared to alternative
solutions, which can be obtained from analytical fundamental waves,
solving the Klein-Gordon equation in an infinite medium. It is shown, how
the Klein-Gordon wave splitting, which transforms the Klein-Gordon equation
into a set of uncoupled first order equations, can be used to adapt the infi-
nite Klein-Gordon solutions to the boundary conditions of the Klein-Gordon
slab. The second example hints at the extensive possibilities offered by the
new method. The current and voltage waves, evoked on the power line after
an imagined strike of lightning, are studied. The non-stationary properties
are modeled by the shunt conductance, which grows exponentially in time,
together with dispersion in the shunt capacitance.
| Original language | English |
|---|---|
| Publisher | [Publisher information missing] |
| Number of pages | 29 |
| Volume | TEAT-7048 |
| Publication status | Published - 1996 |
Publication series
| Name | Technical Report LUTEDX/(TEAT-7048)/1-29/(1996) |
|---|---|
| Volume | TEAT-7048 |
Bibliographical note
Published version: Wave Motion, 27(1), 1-21, 1998.Subject classification (UKÄ)
- Electrical Engineering, Electronic Engineering, Information Engineering
- Other Electrical Engineering, Electronic Engineering, Information Engineering