摘要:

The stability of the steady‐state solution of endothelial cell equation in a mathematical model for tumor angiogenesis is studied. It is proven mathematically that the steady‐state solution is indeed the transition probability function &tgr;(ca,f). Trajectories near the critical point(s) are drawn, and the biological importance of the result is expressed briefly. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814752

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

The Hirota Method, with modified background is applied to construct exact analytical solutions of nonlinear reaction‐diffusion equations of two types. The first equation has only nonlinear reaction part, while the second one has in addition the nonlinear transport term. For both cases, the reaction part has the form of the third order polynomial with three distinct roots. We found analytic one‐soliton solutions and the relationships between three simple roots and the wave speed of the soliton. For the first case, if one of the roots is the mean value of other two roots, the soliton is static. We show that the restriction on three distinct roots to obtain moving soliton is removed in the second case by, adding nonlinear transport term to the first equation. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814753

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

A novel method is developed to construct the Jan‐Teller interaction matrices. The applicability of the method is demonstrated by constructing first and second order Jan‐Teller interaction matrices of theT1⊗ (e⊕t2) octahedral system. The method given here is useful to obtain the Jan‐Teller interaction matrices of the other systems as well as higher order interaction matrices. We also discuss the determination of the location of the stationary points on the potential energy surface, by a successive symmetry breaking of corresponding finite group into its maximal little groups. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814754

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

Modulational instability (also known as the Benjamin‐Feir instability) of quasi‐monochromatic waves propagating in dispersive and weakly nonlinear media is a general phenomenon encountered in hydrodynamics, plasma physics, condensed matter and is responsible for the generation of robust solitary waves (sometime solitons). The statistical approach is reviewed for several nonlinear systems: the nonlinear Schro¨dinger equation, the discrete self‐trapping equation and Ablowitz‐Ladik equation. An integral stability equation is deduced from a linearized kinetic equation for the two‐point correlation function. This is solved for several choices of the unperturbed initial spectral function. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814755

出版商:AIP    

年代:1904

数据来源: AIP