摘要:

The generalized wave equation and generalized sine‐Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two‐dimensional versions. In this paper we associate a system of linear differential equations with these equations and show how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial‐boundary‐value problem is solved for these eq

ISSN:0022-2526    

DOI:10.1002/sapm1986743177

年代:1986

数据来源: WILEY

摘要:

A linear dynamical system is considered whose normal frequencies and normal modes come into close coincidence. The case when both modes have positive energy has been discussed by Grimshaw and Allen (1979). Here the case when one mode has positive energy and the other mode has negative energy is discussed. Coupled equations are derived and solved exactly using parabolic cylinder functions. It is found that the action in both modes grows during the coupling.

ISSN:0022-2526    

DOI:10.1002/sapm1986743205

年代:1986

数据来源: WILEY

摘要:

This paper is concerned with instabilities which develop on a class of parallel shear flows in the presence of a free surface. Implicit in this type of study is the existence of three dimensional instabilities on slightly perturbed two dimensional spatially periodic shear flows.

ISSN:0022-2526    

DOI:10.1002/sapm1986743227

年代:1986

数据来源: WILEY

摘要:

Dendrites of a solid growing steadily in an undercooled melt have a shape given by the solution of certain nonlinear integrodifferential equations. If one does not take account of the Gibbs‐Thomson condition, these equations have an exact solution due to Ivantsov and to Cahn and Horway. For elementary dimensional reasons, the tip velocity in these solutions is left undetermined. This degeneracy is removed by the effect of interface curvature on the melting temperature (Gibbs‐Thomson effect). We show that, in the physically relevant limit of small undercooling, the shape of the dendrite can be deduced from parameterless similarity equations, where the Gibbs‐Thomson effect is included. Every physical quantity is known in this limit, up to a nonlinear eigenvalue that has to be found numeri

ISSN:0022-2526    

DOI:10.1002/sapm1986743245

年代:1986

数据来源: WILEY

摘要:

Saffman's (1985) theory of the superharmonic stability of two‐dimensional irrotational waves on fluid of infinite depth has been generalized to solitary and periodic waves of permanent form on finite uniform depth. The frame of reference for the calculation of the Hamiltonian for periodic waves of finite depth is found to be the frame in which the mean horizontal velocity is zer

ISSN:0022-2526    

DOI:10.1002/sapm1986743259

年代:1986

数据来源: WILEY