摘要:

A set of two coupled nonlinear diffusion reaction equations is studied and the existence of secondary bifurcation is shown. Using the method of two‐timing, it is found that diffusion reaction equations of this type can exhibit an exchange of stability between distinct nontrivial solutions. This exchange can provide either a smooth or discontinuous transition between stable solutions, and the nontrivial solutions can be either steady or temporally periodic. This analysis is applied to the model biochemical reaction of Prigogine and the types of secondary bifurcation which occur in this model are classifie

ISSN:0022-2526    

DOI:10.1002/sapm1976553187

年代:1976

数据来源: WILEY

摘要:

A nonlinear partial difference equation is obtained and solved by the method of inverse scattering. In a certain continuum limit it is shown how this equation approximates the nonlinear Schrodinger equation and a related nonlinear differential‐difference equation. At all times the solutions can be compared, and the scheme is shown to be convergent. These ideas apply to other nonlinear evolution equations as wel

ISSN:0022-2526    

DOI:10.1002/sapm1976553213

年代:1976

数据来源: WILEY

摘要:

The propagation of multiphase modes is considered for the case when group‐velocity projections overlap. Criteria are developed for wave instabilities and for the existence of multiphase solitary envelope solution

ISSN:0022-2526    

DOI:10.1002/sapm1976553231

年代:1976

数据来源: WILEY

摘要:

The caustic formed when a water wave is propagating at incidence into increasing depth is considered first in the linear approximation. A scheme for a nonlinear approach is indicated by this analysis, and the nonlinear equations valid in the caustic region are obtained. Comparison with the gas‐dynamics case shows differences from the equations adopted for the sonic‐boom caus

ISSN:0022-2526    

DOI:10.1002/sapm1976553239

年代:1976

数据来源: WILEY

摘要:

A study is made of a two‐point nonlinear boundary‐value problem with a small parameter multiplying the highest derivative. It is shown that under certain circumstances the asymptotic solution to the problem is expressible in terms of the solution to a linear boundary‐value problem—in which case the two problems are said to be asymptotically equivalent. The coefficients of the linear problem necessarily satisfy certain conditions, and these conditions are shown to bear a close relationship to the equations obtained in constructing a solution to the nonlinear problem by standard matching

ISSN:0022-2526    

DOI:10.1002/sapm1976553249

年代:1976

数据来源: WILEY