Bound States of Interacting Localized Structures
Localized or solitary structures are frequently formed in extended systems under the combined effects of instability and dissipation.1 The effective particle approach widely used for integrable systems2 and in quantum field theory3 can also be used for such systems. Many of the nonlinear PDEs encountered in macroscopic physics can be thus reduced to ODEs that give insight into the full problem, particularly when the original system is invariant under a continuous group. Each solitary structure is assigned a set of the group parameters and these become collective coordinates characterizing the state of the system.4,5
KeywordsLocalize Structure Phase Portrait Homoclinic Orbit Group Parameter Nonlinear PDEs
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