Fluctuations of the reversal point in a stratified-inhomogeneous medium

1973 ◽  
Vol 16 (10) ◽  
pp. 1203-1210
Author(s):  
I. M. Fuks
Keyword(s):  
Inhomogeneous Medium ◽  
Reversal Point

scholarly journals Darboux transformation for classical acoustic spectral problem

2003 ◽  
Vol 2003 (49) ◽  
pp. 3123-3142 ◽  
Author(s):  
A. A. Yurova ◽  
A. V. Yurov ◽  
M. Rudnev
Keyword(s):  
Spectral Problem ◽  
Inhomogeneous Medium ◽  
Darboux Transformation ◽  
Maxwell Equations ◽  
Soliton Solutions ◽  
Moutard Transformation ◽  
Acoustic Problem ◽  
Spatial Dimensions ◽  
Dielectric Permitivity ◽  
Harry Dym Equation

We study discrete isospectral symmetries for the classical acoustic spectral problem in spatial dimensions one and two by developing a Darboux (Moutard) transformation formalism for this problem. The procedure follows steps similar to those for the Schrödinger operator. However, there is no one-to-one correspondence between the two problems. The technique developed enables one to construct new families of integrable potentials for the acoustic problem, in addition to those already known. The acoustic problem produces a nonlinear Harry Dym PDE. Using the technique, we reproduce a pair of simple soliton solutions of this equation. These solutions are further used to construct a new positon solution for this PDE. Furthermore, using the dressing-chain approach, we build a modified Harry Dym equation together with its LA pair. As an application, we construct some singular and nonsingular integrable potentials (dielectric permitivity) for the Maxwell equations in a 2D inhomogeneous medium.

Propagation of thermal waves in an inhomogeneous medium

1981 ◽  
Vol 34 (6) ◽  
pp. 831-852 ◽  
Author(s):  
Shoshana Kamin ◽  
Philip Rosenau
Keyword(s):  
Inhomogeneous Medium ◽  
Thermal Waves
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