Tzitzeica geometry of soliton solutions for quartic interaction PDE
نویسندگان
چکیده
Geometric properties of graphs of solutions for the quartic interaction PDE are studied in the present work. Two classes of solutions are considered. One class is represented by soliton solutions, whereas the other class consists of solutions of a first order PDE system, which generates the quartic interaction PDE, in the sense of least squares type action. We prove that for both classes the graphs of solutions are Tzitzeica flat, i.e., the associated Tzitzeica curvature tensor vanishes. It is also shown how the quartic interaction PDE can be generated using a least squares type action. M.S.C. 2010: 35C08, 53B30, 53Z05.
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