Conservation laws, symmetries, and line soliton solutions of generalized KP and Boussinesq equations with p-power nonlinearities in two dimensions
| Autor: | Anco, S. C., Gandarias, M. L., Recio, E. |
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| Rok vydání: | 2017 |
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| Zdroj: | Theor. and Math. Phys. 196(3) (2018), 1241-1259. Proceedings of the Conference on Physics and Mathematics of Nonlinear Phenomena PMNP2017: 50 years of IST |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1134/S004057791810001X |
| Popis: | Nonlinear generalizations of integrable equations in one dimension, such as the KdV and Boussinesq equations with $p$-power nonlinearities, arise in many physical applications and are interesting in analysis due to critical behaviour. This paper studies analogous nonlinear $p$-power generalizations of the integrable KP equation and the Boussinesq equation in two dimensions. Several results are obtained. First, for all $p\neq 0$, a Hamiltonian formulation of both generalized equations is given. Second, all Lie symmetries are derived, including any that exist for special powers $p\neq0$. Third, Noether's theorem is applied to obtain the conservation laws arising from the Lie symmetries that are variational. Finally, explicit line soliton solutions are derived for all powers $p>0$, and some of their properties are discussed. Comment: Corrected final version |
| Databáze: | arXiv |
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