Adjoint solutions and superposition principle for linearizable Krichever-Novikov equation
Existence of an operator equality for equations connected by nonlocal transformations allowed us to propose a method of finding of a new solution of the initial equation adjoint to its known solution. This approach is used for construction of exact solutions for the linearizable Krichever-Novikov eq...
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| Date: | 2019 |
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| Keywords: | keywords |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| Online Access: | https://trim.imath.kiev.ua/index.php/trim/article/view/375 |
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| Journal Title: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Summary: | Existence of an operator equality for equations connected by nonlocal transformations allowed us to propose a method of finding of a new solution of the initial equation adjoint to its known solution. This approach is used for construction of exact solutions for the linearizable Krichever-Novikov equation and for the corresponding linear equation. The formula of nonlinear nonlocal superposition of solutions for this nonlinear equation is derived and applied to generation of its solutions. |
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