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https://hdl.handle.net/11147/2011
Title: | Soliton resonances for the MKP-II | Authors: | Lee, Jiunhung Pashaev, Oktay |
Keywords: | Derivative reaction-diffusion system Dissipative soliton Hirota method Modified Kadomtsev-Petviashvili equation Soliton resonance |
Publisher: | Pleiades Publishing | Source: | Lee, J., and Pashaev, O. (2005). Soliton resonances for the MKP-II. Theoretical and Mathematical Physics, 144(1), 995-1003. doi:10.1007/s11232-005-0127-5 | Abstract: | 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. | URI: | https://doi.org/10.1007/s11232-005-0127-5 http://hdl.handle.net/11147/2011 |
ISSN: | 0040-5779 0040-5779 1573-9333 |
Appears in Collections: | Mathematics / Matematik Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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