Method of integral equations and an extinction theorem for two-dimensional problems in nonlinear optics

1994 ◽  
Vol 50 (1) ◽  
pp. 714-723 ◽  
Author(s):  
A. V. Ghiner ◽  
G. I. Surdutovich
Keyword(s):  
Nonlinear Optics ◽  
Integral Equations ◽  
Two Dimensional ◽  
Method Of Integral Equations ◽  
Extinction Theorem

Method of integral equations and an extinction theorem in bulk and surface phenomena in nonlinear optics

1994 ◽  
Vol 49 (2) ◽  
pp. 1313-1325 ◽  
Author(s):  
A. V. Ghiner ◽  
G. I. Surdutovich
Keyword(s):  
Nonlinear Optics ◽  
Integral Equations ◽  
Surface Phenomena ◽  
Method Of Integral Equations ◽  
Extinction Theorem

On the Heaving Motion of Cylinders of Shallow Draft

1961 ◽  
Vol 5 (04) ◽  
pp. 34-43
Author(s):  
R. C. MacCamy
Keyword(s):  
Integral Equations ◽  
Circular Disk ◽  
Finite Width ◽  
Two Dimensional ◽  
Virtual Mass ◽  
Method Of Integral Equations ◽  
First Approximation ◽  
Strip Theory ◽  
Considerable Simplification ◽  
Special Case

A perturbation procedure is developed for the two-dimensional motion produced by a long ship in heave when the draft is assumed small. The procedure reduces the shallow draft problem to a series of problems for a "raft" of zero draft. A considerable simplification in the method of integral equations is found to occur. For the first approximation, that is, a raft of finite width, the integral equations are solved numerically to determine pressure, virtual mass and damping. The problem of heave of a circular disk of zero draft is treated by the same methods so that an evaluation of strip theory in this special case is possible.

On steady non-breaking downstream waves and the wave resistance – Stokes’ method

2017 ◽  
Vol 815 ◽  
pp. 388-414
Author(s):  
Dmitri V. Maklakov ◽  
Alexander G. Petrov
Keyword(s):  
Integral Equations ◽  
Wave Amplitude ◽  
Wave Resistance ◽  
Quadratic System ◽  
System Of Equations ◽  
Two Dimensional ◽  
Method Of Integral Equations ◽  
Analytical Formulae ◽  
The Mean ◽  
The Waves

In this work, we have obtained explicit analytical formulae expressing the wave resistance of a two-dimensional body in terms of geometric parameters of nonlinear downstream waves. The formulae have been constructed in the form of high-order asymptotic expansions in powers of the wave amplitude with coefficients depending on the mean depth. To obtain these expansions, the second Stokes method has been used. The analysis represents the next step of the research carried out in Maklakov & Petrov (J. Fluid Mech., vol. 776, 2015, pp. 290–315), where the properties of the waves have been computed by a numerical method of integral equations. In the present work, we have derived a quadratic system of equations with respect to the coefficients of the second Stokes method and developed an effective computer algorithm for solving the system. Comparison with previous numerical results obtained by the method of integral equations has been made.

Sign in / Sign up

Export Citation Format

Share Document