The Motion of Weakly Interacting Pulses in Reaction-Diffusion Systems

By Shin-ichiro Ei. 2002

139 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/30657a9facebbf0535d8c3d4526c7adc876bd4a9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Alain Miranville
2. Bjorn Sandstede
3. Sergey Zelik
4. Arnd Scheel
5. Arjen Doelman
6. Guido Schneider
7. Chunyou Sun
8. Stefanie Sonner

In Statistical and Nonlinear Physics

1. Arjen Doelman
2. Arnd Scheel
3. Bjorn Sandstede
4. Alain Miranville
5. Sergey Zelik
6. Guido Schneider
7. V. D. Ploeg
8. Jerry L. Bona

Citations in the corpus

• Chapter 3 Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains (2008, background): “Then, due to the “tail”-interaction between solitons, a weak temporal dynamics appears and this dynamics allows a center manifold reduction to a lattice system of ODEs (roughly speaking, this system describes the temporal evolution of the soliton centers, see [79,168], and [204] for details).”
• The Dynamics of Modulated Wave Trains (2009, background): “Rigorous results that validate these equations for a finite number of pulse can be found in [14, 47], while their validity for an infinite number of pulses has recently been established in [58].”
• An Explicit Theory for Pulses in Two Component, Singularly Perturbed, Reaction–Diffusion Equations (2015, unknown): “Weak pulse interactions are only driven by exponentially small tail interactions [10, 29, 30].”