Symmetry Operators of the Nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov Equation with a Quadratic Operator

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Abstract

A class of nonlinear symmetry operators has been constructed for the many-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation quadratic in independent variables and derivatives. The construction of each symmetry operator includes an interwining operator for the auxiliary linear equations and additional nonlinear algebraic conditions. Symmetry operators for the one-dimensional equation with a constant influence function have been constructed in explicit form and used to obtain a countable set of exact solutions.

Original languageEnglish
Pages (from-to)1415-1426
Number of pages12
JournalRussian Physics Journal
Volume56
Issue number12
DOIs
Publication statusPublished - 2014

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operators
symmetry
quadratic equations
linear equations

Keywords

  • interwining operator
  • nonlinear symmetry operator
  • nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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title = "Symmetry Operators of the Nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov Equation with a Quadratic Operator",
abstract = "A class of nonlinear symmetry operators has been constructed for the many-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation quadratic in independent variables and derivatives. The construction of each symmetry operator includes an interwining operator for the auxiliary linear equations and additional nonlinear algebraic conditions. Symmetry operators for the one-dimensional equation with a constant influence function have been constructed in explicit form and used to obtain a countable set of exact solutions.",
keywords = "interwining operator, nonlinear symmetry operator, nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation",
author = "Levchenko, {Evgeniy Anatolievich} and Trifonov, {A. Yu} and Shapovalov, {Aleksandr Vasilievich}",
year = "2014",
doi = "10.1007/s11182-014-0194-x",
language = "English",
volume = "56",
pages = "1415--1426",
journal = "Russian Physics Journal",
issn = "1064-8887",
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T1 - Symmetry Operators of the Nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov Equation with a Quadratic Operator

AU - Levchenko, Evgeniy Anatolievich

AU - Trifonov, A. Yu

AU - Shapovalov, Aleksandr Vasilievich

PY - 2014

Y1 - 2014

N2 - A class of nonlinear symmetry operators has been constructed for the many-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation quadratic in independent variables and derivatives. The construction of each symmetry operator includes an interwining operator for the auxiliary linear equations and additional nonlinear algebraic conditions. Symmetry operators for the one-dimensional equation with a constant influence function have been constructed in explicit form and used to obtain a countable set of exact solutions.

AB - A class of nonlinear symmetry operators has been constructed for the many-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation quadratic in independent variables and derivatives. The construction of each symmetry operator includes an interwining operator for the auxiliary linear equations and additional nonlinear algebraic conditions. Symmetry operators for the one-dimensional equation with a constant influence function have been constructed in explicit form and used to obtain a countable set of exact solutions.

KW - interwining operator

KW - nonlinear symmetry operator

KW - nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation

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U2 - 10.1007/s11182-014-0194-x

DO - 10.1007/s11182-014-0194-x

M3 - Article

VL - 56

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JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 12

ER -