Pashaev, Oktay04.02. Department of Mathematics04. Faculty of Science01. Izmir Institute of Technology2023-04-192023-04-19202397830312169922194-1009https://doi.org/10.1007/978-3-031-21700-5_9https://hdl.handle.net/11147/134193rd International Conference on Mathematics and its Applications in Science and Engineering, ICMASE 2022 -- 4 July 2022 through 7 July 2022A new relativistic integrable nonlinear model for real, Majorana type spinor fields in 1+1 dimensions, gauge equivalent to Papanicolau spin model, defined on the one sheet hyperboloid is introduced. By using the double numbers, the model is represented as hyperbolic complex valued relativistic massive Thirring type model. By Hirota’s bilinear method, an exact one and two dissipative soliton solutions of this model are constructed. Calculation of first three integrals of motion for one dissipation solution shows that the last one represents a particle-like nonlinear excitation, with relativistic dispersion and highly nonlinear mass. A nontrivial solution of the system of algebraic equations, showing fusion and fission of relativistic dissipations is found. Asymptotic analysis of exact two dissipaton solution confirms resonant character of our dissipaton interactions. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.eninfo:eu-repo/semantics/openAccessHirota’s methodMajorana spinorRelativistic dissipaton solutionSoliton resonancesAsymptotic analysisConference Object2-s2.0-8515105834810.1007/978-3-031-21700-5_9