EXACT FRONTS FOR THE NONLINEAR DIFFUSION EQUATION WITH QUINTIC NONLINEARITIES

被引：10

作者：

BENGURIA, RD

DEPASSIER, MC

机构：

[1] Facultad de Física, Pontificia Universidad Catlica de Chile, Santiago 22

来源：

PHYSICAL REVIEW E | 1994年 / 50卷 / 05期

关键词：

D O I：

10.1103/PhysRevE.50.3701

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We consider traveling wave solutions of the reaction diffusion equation with quintic nonlinearities ut=uxx+u(1-u)(1+u+u2+u3). If the parameters , , and obey a special relation, then the criterion for the existence of a strong heteroclinic connection can be expressed in terms of two of these parameters. If an additional restriction is imposed, explicit front solutions can be obtained. The approach used can be extended to polynomials whose highest degree is odd. © 1994 The American Physical Society.

引用

收藏

页码：3701 / 3704

页数：4

相关论文

共 13 条

[1] MULTIDIMENSIONAL NON-LINEAR DIFFUSION ARISING IN POPULATION-GENETICS [J].

ARONSON, DG ;

WEINBERGER, HF .

ADVANCES IN MATHEMATICS, 1978, 30 (01) :33-76

[2] VALIDITY OF THE LINEAR SPEED SELECTION MECHANISM FOR FRONTS OF THE NONLINEAR DIFFUSION EQUATION [J].

BENGURIA, RD ;

DEPASSIER, MC .

PHYSICAL REVIEW LETTERS, 1994, 73 (16) :2272-2274

[3] PATTERN PROPAGATION IN NONLINEAR DISSIPATIVE SYSTEMS [J].

BENJACOB, E ;

BRAND, H ;

DEE, G ;

KRAMER, L ;

LANGER, JS .

PHYSICA D-NONLINEAR PHENOMENA, 1985, 14 (03) :348-364

[4] SYMMETRY REDUCTIONS AND EXACT-SOLUTIONS OF A CLASS OF NONLINEAR HEAT-EQUATIONS [J].

CLARKSON, PA ;

MANSFIELD, EL .

PHYSICA D-NONLINEAR PHENOMENA, 1994, 70 (03) :250-288

[5] PROPAGATING PATTERN SELECTION [J].

DEE, G ;

LANGER, JS .

PHYSICAL REVIEW LETTERS, 1983, 50 (06) :383-386

[6] REACTION DIFFUSION-EQUATIONS IN ONE DIMENSION - PARTICULAR SOLUTIONS AND RELAXATION [J].

HERRERA, JJE ;

MINZONI, A ;

ONDARZA, R .

PHYSICA D-NONLINEAR PHENOMENA, 1992, 57 (3-4) :249-266

[7]

KALIAPPAN P, 1992, PHYSICA D, V11, P368

[8]

Kolmogorov AN, 1937, B MGU A, V1, P1, DOI DOI 10.1016/j.jde.2006.04.010

[9] EXACT TRAVELING WAVE SOLUTIONS OF A CLASS OF NONLINEAR DIFFUSION-EQUATIONS BY REDUCTION TO A QUADRATURE [J].

OTWINOWSKI, M ;

PAUL, R ;

LAIDLAW, WG .

PHYSICS LETTERS A, 1988, 128 (09) :483-487

[10] STRUCTURAL STABILITY AND RENORMALIZATION-GROUP FOR PROPAGATING FRONTS [J].

PAQUETTE, GC ;

CHEN, LY ;

GOLDENFELD, N ;

OONO, Y .

PHYSICAL REVIEW LETTERS, 1994, 72 (01) :76-79