Theoretical and Mathematical Physics

, Volume 144, Issue 1, pp 995–1003 | Cite as

Soliton Resonances for the MKP-II

  • J.-H. Lee
  • O. K. Pashaev


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.


soliton resonance dissipative soliton modified Kadomtsev-Petviashvili equation Hirota method derivative reaction-diffusion system 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • J.-H. Lee
    • 1
  • O. K. Pashaev
    • 2
  1. 1.Institute of MathematicsAcademia SinicaTaipeiTaiwan
  2. 2.Department of MathematicsIzmir Institute of TechnologyUrla-IzmirTurkey

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