Theory of group representations and integration of nonlinear systems \(x_{a, z\overline{z}}=\exp(kx)_{a}\)
From MaRDI portal
Publication:995030
DOI10.1016/0167-2789(81)90119-6zbMath1194.37088OpenAlexW2043568615MaRDI QIDQ995030
A. N. Leznov, Mikhail V. Saveliev
Publication date: 13 September 2010
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0167-2789(81)90119-6
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Applications of Lie groups to the sciences; explicit representations (22E70) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)
Related Items
On the integrability problem of a continuous Toda system ⋮ On a family of KP multi-line solitons associated to rational degenerations of real hyperelliptic curves and to the finite non-periodic Toda hierarchy ⋮ From symmetries of partial differential equations towards secondary (``quantized) calculus ⋮ On a solitonic specialisation for the general solutions of some two-dimensional completely integrable systems ⋮ Light-cone parametrizations for Kähler manifolds ⋮ Nonlinear equations and graded Lie algebras ⋮ Maximally non-abelian Toda systems ⋮ General formulas for solutions of initial and boundary-value problems for the sine-Gordon equation ⋮ Combined Wronskian solutions to the 2D Toda molecule equation ⋮ Evolution of Weyl Functions and Initial-Boundary Value Problems ⋮ Harmonic maps and periodic Toda systems ⋮ Sine-Gordon theory in a semi-strip ⋮ Nonlinear \(\sigma\)-models on spheres and Toda systems ⋮ Generalized Toda field theories ⋮ Boundary conditions for two-dimensional integrable chains. ⋮ Soliton solutions for the super mKdV and sinh-Gordon hierarchy ⋮ Holomorphic curves and Toda systems ⋮ The three-colour model with domain wall boundary conditions ⋮ \(W\)-algebras for non-abelian Toda systems ⋮ Coupled systems of nonlinear wave equations and finite-dimensional Lie algebras. I ⋮ Coupled systems of nonlinear wave equations and finite-dimensional Lie algebras. II: A nonlinear system arising from the group \(G_{6,1}\) and its exact integration ⋮ A CLASS OF SPECIAL EXACT SOLUTIONS OF SOME HIGH DIMENSIONAL NON-LINEAR WAVE EQUATIONS ⋮ Wave equations with the characteristic propagation property ⋮ Exactly and completely integrable nonlinear dynamical systems ⋮ Hirota equation and Bethe ansatz ⋮ Group theory approach to the \(\tau\)-function and its quantization ⋮ Solitons, \(\tau\)-functions and Hamiltonian reduction for non-abelian conformal affine Toda theories. ⋮ Tau-functions generating the conservation laws for generalized integrable hierarchies of KdV and affine Toda type ⋮ Multidimensional Toda-type systems ⋮ Two-dimensional exactly and completely integrable dynamical systems ⋮ KP constraints from reduced multi-component hierarchies
Cites Work
