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@article{49266, author = {Opanasenko, Stanislav and Popovych, Roman}, article_location = {Melville (USA)}, article_number = {101515}, doi = {http://dx.doi.org/10.1063/5.0003304}, keywords = {Korteweg-De Vries equation; Classification; Operators; Systems; Fields; Euler}, language = {eng}, issn = {0022-2488}, journal = {Journal of Mathematical Physics}, title = {Generalized symmetries and conservation laws of (1+1)-dimensional Klein-Gordon equation}, url = {https://aip.scitation.org/doi/10.1063/5.0003304}, volume = {61}, year = {2020} }
TY - JOUR ID - 49266 AU - Opanasenko, Stanislav - Popovych, Roman PY - 2020 TI - Generalized symmetries and conservation laws of (1+1)-dimensional Klein-Gordon equation JF - Journal of Mathematical Physics VL - 61 IS - 101515 SP - "101515-1"-"101515-13" EP - "101515-1"-"101515-13" PB - American Institute of Physics SN - 00222488 KW - Korteweg-De Vries equation KW - Classification KW - Operators KW - Systems KW - Fields KW - Euler UR - https://aip.scitation.org/doi/10.1063/5.0003304 N2 - Using advantages of nonstandard computational techniques based on the light-cone variables, we explicitly find the algebra of generalized symmetries of the (1 + 1)-dimensional Klein-Gordon equation. This allows us to describe this algebra in terms of the universal enveloping algebra of the essential Lie invariance algebra of the Klein-Gordon equation. Then, we single out variational symmetries of the corresponding Lagrangian and compute the space of local conservation laws of this equation, which turns out to be generated, up to the action of generalized symmetries, by a single first-order conservation law. Moreover, for every conservation law, we find a conserved current of minimal order contained in this conservation law. ER -
OPANASENKO, Stanislav and Roman POPOVYCH. Generalized symmetries and conservation laws of (1+1)-dimensional Klein-Gordon equation. \textit{Journal of Mathematical Physics}. Melville (USA): American Institute of Physics, 2020, vol.~61, No~101515, p.~''101515-1''-''101515-13'', 13 pp. ISSN~0022-2488. Available from: https://dx.doi.org/10.1063/5.0003304.
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