摘要:

Evolution equations which describe pseudospherical surfaces are considered. A systematic procedure to determine a linear problem for which a given equation is the integrability condition is obtained. The theory is applied to families of equations. In particular, the Liouville equation is obtained as the integrability condition of a linear problem.

ISSN:0022-2526    

DOI:10.1002/sapm1987772103

年代:1987

数据来源: WILEY

摘要:

Lete(x, t) =∑pn(x)tnbe the generating function of a polynomial sequence, and the transform of multiplication byxrelative toe(x, t). We show that the sequencepn(x) is orthogonal precisely when is at‐variable, i.e., mapsK[t] into itself and increases degree by 1. We also show how transform techniques can shed light on the recursion relations and differential equations forpn

ISSN:0022-2526    

DOI:10.1002/sapm1987772119

年代:1987

数据来源: WILEY

摘要:

The time‐dependent, nonlinear, viscous critical‐layer problem posed by Gajjar and Smith is studied analytically and numerically, for various values of the time‐dependence parameterµand the viscous parameterγc, to help to complete the understanding of the solution. The analysis concerns the nearly inviscid limitγc→ 0 which corresponds to increasing disturbance amplitude, other limits for weaker disturbances having been studied previously. On the numerical side, computational results obtained for order‐1 valuesof µ,γcare described and are compared with analytical predictions. Particular attention is given to the phase shift produced across the

ISSN:0022-2526    

DOI:10.1002/sapm1987772129

年代:1987

数据来源: WILEY

摘要:

Explicit series formulae are given for use in the method of steepest descents, where it is required to find the contribution to an integral of the form∫evw(z)φ(z)dzfrom a well‐isolated saddle pointz0. Here v is a large positive parameter, andw(N)(z0) ≠ 0 while lower‐order derivatives atz0are equal to zero. Examples where the formulae are helpful are p

ISSN:0022-2526    

DOI:10.1002/sapm1987772151

年代:1987

数据来源: WILEY

摘要:

The electric and magnetic fields within optical thin films are obtained exactly in closed form as solutions of a system of difference equations presented by Berning and utilized by Dill, Neureuther, Tuttle, and Walker in theirsampleprogram for modeling optical lithography. The solution allows an explicit closed form expression for the absorbance.

ISSN:0022-2526    

DOI:10.1002/sapm1987772173

年代:1987

数据来源: WILEY