Asymptotics of the Spectrum of a Two-dimensional Hartree Type Operator Near Upper Boundaries of Spectral Clusters. Asymptotic Solutions Located Near a Circle

2017 ◽  
Vol 226 (4) ◽  
pp. 517-530 ◽  
Author(s):  
A. V. Pereskokov
Keyword(s):  
Type Operator ◽  
Asymptotic Solutions ◽  
Two Dimensional

Asymptotic Solutions and Radiation Conditions for Second-Order Diffracted Waves

1989 ◽  
Vol 111 (3) ◽  
pp. 203-207
Author(s):  
H. Huang ◽  
J. Li ◽  
X. Wang
Keyword(s):  
Finite Element ◽  
Circular Cylinder ◽  
Second Order ◽  
Asymptotic Solutions ◽  
Wave Forces ◽  
Far Field ◽  
Two Dimensional ◽  
Diffracted Waves ◽  
Artificial Boundaries ◽  
Radiation Conditions

The far-field asymptotic solutions for the second-order diffracted waves have been developed, both in three and two-dimensional problems. The radiation conditions for the second-order diffracted waves are derived by using the asymptotic solutions. The nonlinear wave forces on a half-circular cylinder on seabed are presented by using finite element methods with the radiation conditions imposed on the artificial boundaries.

Ein einfaches Inkrementenverfahren zur Bestimmung der Ladungen in nichtaromatischen Molekiilen

1984 ◽  
Vol 39 (11) ◽  
pp. 1082-1088
Author(s):  
Wolfgang Schleker ◽  
Burghard Schmidt ◽  
Wilhelm Mertens ◽  
Jörg Fleischhauer
Keyword(s):  
Small Perturbation ◽  
Perturbation Analysis ◽  
Numerical Solutions ◽  
Asymptotic Solutions ◽  
Polar Coordinates ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Whitham Equations

The Chester-Chisnell-Whitham equations in Cartesian and polar coordinates are written out for the two-dimensional case. The solution expanded near a point is obtained. The asymptotic solutions of order 2 near focus are presented. Linear small perturbation analysis for a converging cylindrical shock is given. To study the development of perturbations numerical solutions are carried out.

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