caa a22 4500 477097480 CHVBK 20180405111531.0 cr unu---uuuuu 170330e19960701xx s 000 0 eng 10.1007/BF02996018 doi (NATIONALLICENCE)springer-10.1007/BF02996018 Zagrodzinski Jerzy Institute of Physics, Polish Academy of Sciences, 02-668, Warsaw, Poland aut Multiperiodic processes of soliton type with application to physics [Elektronische Daten] [Jerzy Zagrodzinski] Processus MultipÉriodiques du Type Soliton et Leurs Applications À la Physique The aim of the present review paper is to show how periodic processes and localized excitations can be simultaneously incorporated into nonlinear equations of soliton type. Starting from perturbative approach it is shown that for all classes of soliton type equations i.e. partial derivative, ordinary derivative and functional equations there can exist exact solutions in form of solitons on the background of quasiperiodic process. These solutions are useful if one wants to discuss a signal with noise in nonlinear systems. From mathematical point of view the simplest way to handle such situations in soliton type equations is the dispersion equation formalism which proves also that a noise makes a dominant part of solution. The role of modular transformation and its relation with transformations on Riemann surfaces suitable for a description of quasi-periodic processes in soliton type equations is also discussed. As an application, a fully nonlinear approach to a long Josephson junction and its consequences are discussed. Institut Telecom / Springer-Verlag France, 1996 Non linear equation nationallicence Soliton nationallicence Mathematical physics nationallicence Differential equation nationallicence Partial derivative equation nationallicence Functional equation nationallicence Riemann geometry nationallicence Super conducting junction nationallicence Josephson effect nationallicence Background noise nationallicence Equation non linéaire nationallicence Soliton nationallicence Physique mathématique nationallicence Equation différientelle nationallicence Equation dérivée partielle nationallicence Equation fonctionnelle nationallicence Géométrie Riemann nationallicence Jonction supraconductrice nationallicence Effet Josephson nationallicence Bruit fond nationallicence Annales Des Télécommunications Springer-Verlag 51/7-8(1996-07-01), 304-312 0003-4347 51:7-8<304 1996 51 12243 https://doi.org/10.1007/BF02996018 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02996018 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Zagrodzinski Jerzy Institute of Physics, Polish Academy of Sciences, 02-668, Warsaw, Poland aut NATIONALLICENCE 773 0- Annales Des Télécommunications Springer-Verlag 51/7-8(1996-07-01), 304-312 0003-4347 51:7-8<304 1996 51 12243 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer