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February 2007 Dynamics of traveling pulses in heterogeneous media of jump type
Yasumasa NISHIURA, Yoshihito OYAMA, Kei-ichi UEDA
Hokkaido Math. J. 36(1): 207-242 (February 2007). DOI: 10.14492/hokmj/1285766659


We study pulse dynamics in one-dimensional heterogeneous media. In particular we focus on the case where the pulse is close to the singularity of codim 2 type consisting of drift and saddle-node instabilities in a parameter space. We assume that the heterogeneity is of jump type, namely one of the coefficients of the system undergoes an abrupt change at one point in the space. Depending on the height of this jump, the responses of pulse behavior are penetration, splitting, and rebound. Taking advantage of the fact that pulse is close to the singularity, the PDE dynamics can be reduced to a finite-dimensional system, which displays the three behaviors. Moreover it takes a universal form independent of model systems, and is valid for much more general heterogeneities such as bump, periodic, and random cases.


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Yasumasa NISHIURA. Yoshihito OYAMA. Kei-ichi UEDA. "Dynamics of traveling pulses in heterogeneous media of jump type." Hokkaido Math. J. 36 (1) 207 - 242, February 2007.


Published: February 2007
First available in Project Euclid: 29 September 2010

zbMATH: 1145.35021
MathSciNet: MR2309830
Digital Object Identifier: 10.14492/hokmj/1285766659

Primary: 34C37
Secondary: 35B32 , 35K57

Keywords: Bifurcation (35B32) , Homoclinic and Heteroclinic solutions (34C37) , reaction-diffusion equations (35K57)

Rights: Copyright © 2007 Hokkaido University, Department of Mathematics


Vol.36 • No. 1 • February 2007
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