摘要:

The group theoretical explanation is given of the quasisolution method for partial differential equations recently introduced by Rubel. The examples show that the group approach is simpler from the computational point of view.

ISSN:0022-2526    

DOI:10.1002/sapm1995943211

年代:1995

数据来源: WILEY

摘要:

Any weak, steady vortical flow is a solution, to leading order, of the inviscid fluid equations with a free surface, so long as this flow has horizontal streamlines coinciding with the undisturbed free surface. This work considers the propagation of long irrotational surface gravity waves when such a vortical flow is present. In particular, when the vortical flow and the irrotational surface waves are both periodic and have comparable length scales, resonant interactions can occur between the various components of the flow. The interaction is described by two coupled Korteweg‐de Vries equations and a two‐dimensional streamfunction equat

ISSN:0022-2526    

DOI:10.1002/sapm1995943225

年代:1995

数据来源: WILEY

摘要:

We consider the nonlinear Schrödinger equation perturbed by the addition of a third‐derivative term whose coefficient constitutes a small parameter. It is known from the work of Wai et al. [1] that this singular perturbation causes the solitary wave solution of the nonlinear Schrödinger equation to become nonlocal by the radiation of small‐amplitude oscillatory waves. The calculation of the amplitude of these oscillatory waves requires the techniques of exponential asymptotics. This problem is re‐examined here and the amplitude of the oscillatory waves calculated using the method of Borel summation. The results of Wai et al. [1]are modified and e

ISSN:0022-2526    

DOI:10.1002/sapm1995943257

年代:1995

数据来源: WILEY

摘要:

Asymptotic and numerical methods are used to study several classes of singularly perturbed boundary value problems for which the underlying homogeneous operators have exponentially small eigenvalues. Examples considered include the familiar boundary layer resonance problems and some extensions and certain linearized equations associated with metastable internal layer motion. For the boundary layer resonance problems, a systematic projection method, motivated by the work of De Groen [1], is used to analytically calculate high‐order asymptotic solutions. This method justifies and extends some previous results obtained from the variational method of Grasman and Matkowsky [2]. A numerical approach, based on an integral equation formulation, is used to accurately compute boundary layer resonance solutions and their associated exponentially small eigenvalues. For various examples, the numerical results are shown to compare very favorably with two‐term asymptotic results. Finally, some Sturm‐Liouville operators with exponentially small spectral gap widths are studied. One such problem is applied to analyzing metastable internal layer motion for a certain forced Burgers equ

ISSN:0022-2526    

DOI:10.1002/sapm1995943271

年代:1995

数据来源: WILEY

摘要:

We introduce the notion of cyclic tableaux and develop involutions for Waring's formulas expressing the power sum symmetric functionpnin terms of the elementary symmetric functionenand the homogeneous symmetric functionhn. The coefficients appearing in Waring's formulas are shown to be a cyclic analog of the multinomial coefficients, a fact that seems to have been neglected before. Our involutions also spell out the duality between these two forms of Waring's formulas, which turns out to be exactly the “duality between sets and multisets.” We also present an involution for permutations in cycle notation, leading to probably the simplest combinatorial interpretation of the Möbius function of the partition lattice and a purely combinatorial treatment of the fundamental theorem on symmetric functions. This paper is motivated by Chebyshev polynomials in connection with Waring's formula in two varia

ISSN:0022-2526    

DOI:10.1002/sapm1995943327

年代:1995

数据来源: WILEY

摘要:

This paper establishes a nonlinear energy stability theory for the double‐diffusive convection in a porous medium when both viscosity and thermal expansion coefficient are allowed to vary with temperature. After presenting a nonlinear stability theorem, a variational problem is formulated and the numerical solutions via the compoound matrix method are carried out. It is noted that higher values of the thermal coefficient and higher values of the viscosity ratio have the effect of delaying the onset of convectio

ISSN:0022-2526    

DOI:10.1002/sapm1995943341

年代:1995

数据来源: WILEY