Open Access
2015 On the Soliton Solutions of a Family of Tzitzeica Equations
Corina N. Babalic, Radu Constantinescu, Vladimir S. Gerdjikov
J. Geom. Symmetry Phys. 37: 1-24 (2015). DOI: 10.7546/jgsp-37-2015-1-24


We analyze several types of soliton solutions to a family of Tzitzeica equations. To this end we use two methods for deriving the soliton solutions: the dressing method and Hirota method. The dressing method allows us to derive two types of soliton solutions. The first type corresponds to a set of 6 symmetrically situated discrete eigenvalues of the Lax operator $L$; to each soliton of the second type one relates a set of 12 discrete eigenvalues of $L$. We also outline how one can construct general $N$ soliton solution containing $N_1$ solitons of first type and $N_2$ solitons of second type, $N=N_1+N_2$. The possible singularities of the solitons and the effects of change of variables that relate the different members of Tzitzeica family equations are briefly discussed. All equations allow quasi-regular as well as singular soliton solutions.


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Corina N. Babalic. Radu Constantinescu. Vladimir S. Gerdjikov. "On the Soliton Solutions of a Family of Tzitzeica Equations." J. Geom. Symmetry Phys. 37 1 - 24, 2015.


Published: 2015
First available in Project Euclid: 27 May 2017

zbMATH: 1325.35188
MathSciNet: MR3362493
Digital Object Identifier: 10.7546/jgsp-37-2015-1-24

Rights: Copyright © 2015 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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