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Algebraic operator method for the construction of solitary solutions to nonlinear differential equations |
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| Authors: | Zenonas Navickas Liepa Bikulciene Maido Rahula Minvydas Ragulskis |
| Affiliation: | 1. Department of Applied Mathematics, Kaunas University of Technology, Studentu 50-325, LT-51368 Kaunas, Lithuania;2. Institute of Pure Mathematics, Tartu University, J. Liivi 2-427, Tartu EE-50409, Estonia;3. Research Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-222, Kaunas LT-51368, Lithuania |
| Abstract: | Solutions of the KdV equation are derived by the algebraic operator method based on generalized operators of differentiation. The algebraic operator method based on the generalized operator of differentiation is exploited for the derivation of analytic solutions to the KdV equation. The structure of solitary solutions and explicit conditions of existence of these solutions in the subspace of initial conditions are derived. It is shown that special solitary solutions exist only on a line in the parameter plane of initial and boundary conditions. This new theoretical result may lead to important findings in a variety of practical applications. |
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