We explore the possibility of using soliton interactions in a one-dimensional
\nbulk medium as a basis for a new kind of computer. Such a structure
\nis gateless” { all computations are determined by an input stream
\nof solitons. Intuitively, the key requirement for accomplishing this is that
\nsoliton collisions be nonoblivious; that is, solitons should transfer state
\ninformation during collisions. All the well known systems described by
\nintegrable partial di erential equations (PDEs) { the Korteweg-de Vries,
\nsine-Gordon, cubic nonlinear Schrodinger, and perhaps all integrable systems
\n{ are oblivious when displacement or phase is used as state. We
\npresent a cellular automaton (CA) model, the oblivious soliton machine
\n(OSM), which captures the interaction of solitons in systems described by
\nsuch integrable PDEs. We then prove that OSMs with either quiescent
\nor periodic backgrounds can do only computation that requires time at
\nmost cubic in the input size, and thus are far from being computationuniversal.
\nNext, we de ne a more general class of CA, soliton machines
\n(SMs), which describe systems with more complex interactions. We show
\nthat an SM with a quiescent background can have at least the computational
\npower of a nite-tape Turing machine, whereas an SM with a
\nperiodic background can be universal. The search for useful nonintegrable
\n(and nonoblivious) systems is challenging: We must rely on numerical
\nsolution, collisions may be at best only near-elastic, and collision elasticity
\nand nonobliviousness may be antagonistic qualities. As a step in this
\ndirection, we show that the logarithmically nonlinear Schrodinger equation
\n(log-NLS) supports quasi-solitons (gaussons) whose collisions are, in
\nfact, very near-elastic and strongly nonoblivious. It is an open question
\nwhether there is a physical system that realizes a computation-universal
\nsoliton machine.<\/p>\n","protected":false},"excerpt":{"rendered":"
We explore the possibility of using soliton interactions in a one-dimensional bulk medium as a basis for a new kind of computer. Such a structure is gateless” { all computations are determined by an input stream of solitons. Intuitively, the key requirement for accomplishing this is that soliton collisions be nonoblivious; that is, solitons should […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"Complex Systems","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"1","msr_journal":"Complex Systems","msr_number":"1","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"10","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Ken Steiglitz, Richard K. 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