Lie theory and separation of variables. 10. Nonorthogonal R-separable solutions of the wave equation ∂ttψ=Δ2ψ

1976 ◽  
Vol 17 (3) ◽  
pp. 356 ◽  
Author(s):  
E. G. Kalnins
Keyword(s):  
Wave Equation ◽  
Separation Of Variables ◽  
Lie Theory

scholarly journals Lie theory and separation of variables. 4. The groups SO (2,1) and SO (3)

1974 ◽  
Vol 15 (8) ◽  
pp. 1263-1274 ◽  
Author(s):  
E. G. Kalnins ◽  
Willard Miller
Keyword(s):  
Separation Of Variables ◽  
Lie Theory

A Perturbation Method for Low-Frequency Fluid-Structure Interaction Problems

1973 ◽  
Vol 40 (2) ◽  
pp. 388-394 ◽  
Author(s):  
Y. K. Lou
Keyword(s):  
Wave Equation ◽  
Perturbation Method ◽  
Electromagnetic Scattering ◽  
Perturbation Methods ◽  
Separation Of Variables ◽  
Fluid Structure Interaction ◽  
Low Frequency ◽  
Approximate Solutions ◽  
Fluid Structure ◽  
Structure Interaction

Perturbation methods have been used for electromagnetic scattering and diffraction problems in recent years. A similar method suitable for low-frequency fluid-structure interaction problems is presented. The essence of the method lies in the fact that approximate solutions for fluid-structure interaction problems can be obtained from a set of Poisson’s equations, rather than from the reduced wave equation. The method is particularly useful for those problems where the Poisson’s equation may be solved by the method of separation of variables while the reduced wave equation cannot. As an illustrative example, the vibrations of a submerged spherical shell is studied using the perturbation method and the accuracy of the method is demonstrated.

Separation of variables in the wave equation. Sets of the type (1.1) and Schr�dinger equation

1991 ◽  
Vol 34 (2) ◽  
pp. 122-126
Author(s):  
V. G. Bagrov ◽  
B. F. Samsonov ◽  
A. V. Shapovalov
Keyword(s):  
Wave Equation ◽  
Separation Of Variables ◽  
Dinger Equation
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