Maps, PDE's and Solitary Waves

Troy Shinbrot; J. M. Ottino

doi:10.1142/s0218127495000429

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arXiv · solv-int/9410002

Maps, PDE's and Solitary Waves

Troy Shinbrot·J. M. Ottino

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Abstract

We describe a map-based model which reproduces many of the behaviors seen in partial differential equations (PDE's). Like PDE's, we show that this model can support an infinite number of stationary solutions, traveling solutions, breathing solutions, and elastically colliding solutions. Unlike PDE's, the model can be applied with minimal computational machinery, and few sources of numerical error. Moreover, this model clarifies possible mechanisms by which various coherent solutions are maintained in the face of dispersion.

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solv-int chao-dyn nlin.CD nlin.PS nlin.SI patt-sol

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Troy Shinbrot, J. M. Ottino. 1994-10-13. Maps, PDE's and Solitary Waves. https://doi.org/10.1142/s0218127495000429

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