Equations of arbitrary order invariant under the Kadomtsev–Petviashvili symmetry group

DOI10.1063/1.1645651zbMath1070.37048OpenAlexW2075438661MaRDI QIDQ4833344

Xiao-yan Tang, Sen-yue Lou

Publication date: 15 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1645651

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Geometric theory, characteristics, transformations in context of PDEs (35A30)

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Cites Work

• Search for high dimensional integrable models
• Generalized Kadomtsev-Petviashvili equation with an infinite-dimensional symmetry algebra
• \((3+1)\)-dimensional models with an infinitely dimensional Virasoro type symmetry algebra
• Symmetry reduction for the Kadomtsev–Petviashvili equation using a loop algebra
• Lie symmetries of Hirota’s bilinear equations
• Symmetries of the Kadomtsev-Petviashvili equation
• Generalized symmetries and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">w</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">∞</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>algebras in three-dimensional Toda field theory
• Virasoro structure and localized excitations of the LKR system
• Generalized symmetries and algebras of the two-dimensional differential-difference Toda equation
• (2+1)-dimensional models with Virasoro-type symmetry algebra

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