Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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  • Article
    Relativistic Dissipatons in Integrable Nonlinear Majorana Type Spinor Model
    (Yunnan University, 2022) Pashaev, Oktay; Lee, J. H.
    By method of moving frame, the relativistic integrable nonlinear model for real, Majorana type spinor fields in 1+1 dimensions is introduced and gauge equivalence of this model with Papanicolau spin model on one sheet hyperboloid is established. In terms of the so called double numbers, the model is represented also as hyperbolic complex relativistic model, in the form similar to the massive Thirring model. By using Hirota's bilinear method, the one dissipaton solution of this model is constructed. We calculate first integrals of motion for this dissipaton and show that it represents a relativistic particle with highly nonlinear mass. Analyzing resonance conditions for scattering of two relativistic dissipatons, we find a solution describing resonant property of the dissipatons.
  • Conference Object
    Citation - WoS: 8
    Citation - Scopus: 7
    Soliton Resonances for the Mkp-Ii
    (Pleiades Publishing, 2005) Lee, Jiunhung; Pashaev, Oktay
    Using the second flow (derivative reaction-diffusion system) and the third one of the dissipative SL(2, ℝ) Kaup-Newell hierarchy, we show that the product of two functions satisfying those systems is a solution of the modified Kadomtsev-Petviashvili equation in 2+1 dimensions with negative dispersion (MKP-II). We construct Hirota's bilinear representations for both flows and combine them as the bilinear system for the MKP-II. Using this bilinear form, we find one- and two-soliton solutions for the MKP-II. For special values of the parameters, our solution shows resonance behavior with the creation of four virtual solitons. Our approach allows interpreting the resonance soliton as a composite object of two dissipative solitons in 1+1 dimensions.
  • Conference Object
    Citation - WoS: 16
    Citation - Scopus: 14
    Degenerate Four-Virtual Resonance for the Kp-Ii
    (Pleiades Publishing, 2005) Pashaev, Oktay; Francisco, Meltem L. Y.
    We propose a method for solving the (2+1)-dimensional Kadomtsev- Petviashvili equation with negative dispersion (KP-II) using the second and third members of the disipative version of the AKNS hierarchy. We show that dissipative solitons (dissipatons) of those members yield the planar solitons of the KP-II. From the Hirota bilinear form of the SL(2,ℝ) AKNS flows, we formulate a new bilinear representation for the KP-II, by which we construct one- and two-soliton solutions and study the resonance character of their mutual interactions. Using our bilinear form, for the first time, we create a four-virtual-soliton resonance solution of the KP-II, and we show that it can be obtained as a reduction of a four-soliton solution in the Hirota-Satsuma bilinear form for the KP-II