摘要:

The Painlevé property of annth‐order differential equation is that no solution has any movable singularities other than poles. This property is strongly indicative of complete integrability (the existence ofn− 1 integrals). However, the usual technique employed to test for the Painlevé property seeks only movable algebraic (or logarithmic) singularities. More general singularities are ignored. But, the six standard Painlevé equations are known to have no such singularities. Painlevé's proof of this is long and laborious; we give here a direc

ISSN:0022-2526    

DOI:10.1002/sapm1994933187

年代:1994

数据来源: WILEY

摘要:

Convective motion in a layer of fluid heated from below is considered where the boundaries are stress free and the upper surface supports interfacial gravity waves. Inviscid, immiscible, constant density, ambient fluid is separated from the convecting layer below by a stable density jump. An important parameter in the problem isδrepresenting the ratio of the interfacial density jump to the density change across the convecting layer. Amplitude equations are derived describing convective motion in the plane and a planform selection analysis performed. It is demonstrated that the breaking of the translational and Galilean invariance of the problem allows a strong coupling between a large‐scale interfacial mode and convection. The resulting phase dynamics is third order in ti

ISSN:0022-2526    

DOI:10.1002/sapm1994933209

年代:1994

数据来源: WILEY

摘要:

A comprehensive exact treatment of free surface flows governed by shallow water equations (in sigma variables) is given. Several new families of exact solutions of the governing PDEs are found and are shown to embed the well‐known self‐similar or traveling wave solutions which themselves are governed by reduced ODEs. The classes of solutions found here are explicit in contrast to those found earlier in an implicit form. The height of the free surface for each family of solutions is found explicitly. For the traveling or simple wave, the free surface is governed by a nonlinear wave equation, but is arbitrary otherwise. For other types of solutions, the height of the free surface is constant either on lines of constant acceleration or on lines of constant speed; in another case, the free surface is a horizontal plane while the flow underneath is a sine wave. The existence of simple waves on shear flows is analytically proved. The interaction of large amplitude progressive waves with shear flow is also stud

ISSN:0022-2526    

DOI:10.1002/sapm1994933251

年代:1994

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1994933275

年代:1994

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1994933279

年代:1994

数据来源: WILEY