Two-Dimensional Toda Lattice Equations

AbstractWe associate to each complex simple Lie algebra g a hierarchy of evolution equations; in the simplest case g = sl(2) they are the modified KdV equations. These new equations are related to the two-dimensional Toda lattice equations associated with g in the same way that the modified KdV equations are related to the sinh-Gordon equation.

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Derivation and solution of the two dimensional Toda lattice equations by use of the Iwasawa decomposition

Journal of Physics A General Physics ◽

10.1088/0305-4470/15/1/014 ◽

1982 ◽

Vol 15 (1) ◽

pp. 25-46 ◽

Cited By ~ 9

Author(s):

R S Farwell ◽

M Minami

Keyword(s):

Toda Lattice ◽

Iwasawa Decomposition ◽

Two Dimensional ◽

Toda Lattice Equations

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Solutions of Two- and Three-Dimensional Toda Lattice Equations in Terms of Various Forms of Bessel Functions

Journal of the Physical Society of Japan ◽

10.1143/jpsj.54.3701 ◽

1985 ◽

Vol 54 (10) ◽

pp. 3701-3707 ◽

Cited By ~ 9

Author(s):

Noriko Saitoh ◽

Shozo Takeno ◽

Éi Iti Takizawa

Keyword(s):

Bessel Functions ◽

Toda Lattice ◽

Three Dimensional ◽

Toda Lattice Equations

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A Transformation Connecting the Two-Dimensional Toda Lattice and K-dV Equation

Journal of the Physical Society of Japan ◽

10.1143/jpsj.57.2685 ◽

1988 ◽

Vol 57 (8) ◽

pp. 2685-2688 ◽

Cited By ~ 4

Author(s):

Michiaki Matsukawa ◽

Shinsuke Watanabe

Keyword(s):

Toda Lattice ◽

Two Dimensional

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A Rational Flow for the Toda Lattice Equations

Operators, Systems and Linear Algebra - European Consortium for Mathematics in Industry ◽

10.1007/978-3-663-09823-2_4 ◽

1997 ◽

pp. 33-44 ◽

Cited By ~ 4

Author(s):

Roger W. Brockett

Keyword(s):

Toda Lattice ◽

Toda Lattice Equations

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A class of solutions of the two-dimensional Toda lattice equation

Physics Letters A ◽

10.1016/j.physleta.2020.126979 ◽

2021 ◽

Vol 385 ◽

pp. 126979

Author(s):

V.N. Duarte

Keyword(s):

Toda Lattice ◽

Two Dimensional ◽

Lattice Equation ◽

Toda Lattice Equation

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A New Bäcklund Transformation of the Two-Dimensional Toda Lattice

Journal of the Physical Society of Japan ◽

10.1143/jpsj.55.1827 ◽

1986 ◽

Vol 55 (6) ◽

pp. 1827-1835 ◽

Cited By ~ 7

Author(s):

Noriko Saitoh ◽

Éi Iti Takizawa

Keyword(s):

Toda Lattice ◽

Bäcklund Transformation ◽

Two Dimensional ◽

Backlund Transformation

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On the Solutions of the Linear Bäcklund Transformation of the Two-Dimensional Toda Lattice Equation

Journal of the Physical Society of Japan ◽

10.1143/jpsj.56.3813 ◽

1987 ◽

Vol 56 (11) ◽

pp. 3813-3820 ◽

Cited By ~ 1

Author(s):

Fukuko Yuasa ◽

Noriko Saitoh ◽

Éi Iti Takizawa

Keyword(s):

Toda Lattice ◽

Bäcklund Transformation ◽

Two Dimensional ◽

Backlund Transformation ◽

Lattice Equation ◽

Toda Lattice Equation

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Darboux transformation and two-dimensional Toda lattice

Journal of Soviet Mathematics ◽

10.1007/bf01084172 ◽

1983 ◽

Vol 23 (4) ◽

pp. 2441-2446 ◽

Cited By ~ 4

Author(s):

V. B. Matveev ◽

M. A. Salle

Keyword(s):

Darboux Transformation ◽

Toda Lattice ◽

Two Dimensional

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Five-Dimensional Gauge Theories and Whitham–Toda Equation

Modern Physics Letters A ◽

10.1142/s0217732397002235 ◽

1997 ◽

Vol 12 (29) ◽

pp. 2183-2191 ◽

Cited By ~ 1

Author(s):

Masato Hisakado

Keyword(s):

Gauge Theory ◽

Toda Lattice ◽

Gauge Theories ◽

Toda Chain ◽

Charge Conjugation ◽

Two Dimensional ◽

Toda Equation ◽

Toda Lattice Hierarchy

The five-dimensional supersymmetric SU (N) gauge theory is studied in the framework of the relativistic Toda chain. This equation can be embedded in two-dimensional Toda lattice hierarchy. This system has the conjugate structure which corresponds to the charge conjugation.

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