摘要:

A dynamical system with weak nonlinearity is considered for the situation when three modes come into resonance. Interaction equations are derived, and various analytical approximations and numerical results obtained. If is found that either the interaction is explosive, when all modes generally grow during the interaction, with the possibility of an algebraic singularity developing, or the interaction is contained, and the modes exchange action during the coupling. The explosive interaction requires both positive‐ and negative‐energy modes to participate, while the contained interaction can accommodate modes with the same‐sign or opposite‐sign e

ISSN:0022-2526    

DOI:10.1002/sapm19877711

年代:1987

数据来源: WILEY

摘要:

Motivated by recent work on the generalized wave and Sine‐Gordon equatons, various multidimensional extensions of the classical self‐dual Yang‐Mills equation are developed. A method to obtain a broad class of solutions is

ISSN:0022-2526    

DOI:10.1002/sapm198777137

年代:1987

数据来源: WILEY

摘要:

Using the existence of a principal five‐dimensional subalgebra for several types of basic Lie superalgebras, the unimodality of the principally specialized character of a typical finite‐dimensional module with highest weight Λ is derived. This gives rise to some remarkable unimodal partition polynom

ISSN:0022-2526    

DOI:10.1002/sapm198777147

年代:1987

数据来源: WILEY

摘要:

Carrier and Pearson introduced a nonlinear singularly perturbed boundary value problem that has served as a paradigm for problems where the method of matched asymptotic expansions (MAE) apparently fails. The “failure” of MAE is its inability to select the location of possible internal layers, though their structure is determined. Thus, a straightforward application of MAE leaves the positions of any internal layers arbitrary, though the asymptotic expansion of the exact solution to the problem exhibits internal layers only at specific locations. For this reason the solutions produced by MAE have been referred to as spurious solutions. We resolve the question of finding the positions of the interior layers by employing the variational approach of Grasman and Matkowsky. In addition, we show that this method tells how solutions bifurcate as the boundary values are varied, and give an alternative motivation for the variational approach via Newton”s m

ISSN:0022-2526    

DOI:10.1002/sapm198777161

年代:1987

数据来源: WILEY

摘要:

The partition function of the two‐dimensional Ising model in the presence of a magnetic field is expressed as a fourfold integral of a double product of elementary functions. The correlation functions and the magnetization per site are obtained as wel

ISSN:0022-2526    

DOI:10.1002/sapm198777189

年代:1987

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1987771101

年代:1987

数据来源: WILEY