The lie algebra of invariant group of the KdV, MKdV, or Burgers equation

1979 ◽  
Vol 3 (5) ◽  
pp. 387-393 ◽  
Author(s):  
Tu Gue-Zhang
Keyword(s):  
Lie Algebra ◽  
Burgers Equation ◽  
Invariant Group

Lie algebra of coupled higher-dimensional forced Burgers’ equation

2021 ◽  
Author(s):  
Amlan K. Halder ◽  
Kyriakos Charalambous ◽  
R. Sinuvasan ◽  
P. G. L. Leach
Keyword(s):  
Lie Algebra ◽  
Burgers Equation ◽  
Higher Dimensional

CASORATIAN SOLUTIONS AND NEW SYMMETRIES OF THE DIFFERENTIAL-DIFFERENCE KADOMTSEV–PETVIASHVILI EQUATION

2009 ◽  
Vol 23 (17) ◽  
pp. 2107-2114 ◽  
Author(s):  
DA-JUN ZHANG ◽  
JIE JI ◽  
XIAN-LONG SUN
Keyword(s):  
Lie Algebra ◽  
Three Dimensional ◽  
Single Parameter ◽  
Petviashvili Equation ◽  
Invariant Group

This paper first discusses the condition in which Casoratian entries satisfy for the differential-difference Kadomtsev–Petviashvili equation. Then from the Casoratian condition we find a transformation under which the differential-difference Kadomtsev–Petviashvili equation is invariant. The transformation, consisting of a combination of Galilean and scalar transformations, provides a single-parameter invariant group for the equation. We further derive the related symmetry, and the symmetry together with other two symmetries form a closed three-dimensional Lie algebra.

Hamiltonian Systems Based on a Lie Algebra

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Lie Algebra ◽  
Euler Equations ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Three Dimensional ◽  
Hamiltonian Formalism ◽  
Virasoro Algebra ◽  
Inner Product ◽  
The Kdv Equation ◽  
Limiting Case

There is a remarkable analogy between Euler’s equations for a rigid body and his equations for an ideal fluid. The unifying idea is that of a Lie algebra with an inner product, which is not invariant, on it. The concepts of a vector space, Lie algebra, and inner product are reviewed. A hamiltonian dynamical system is derived from each metric Lie algebra. The Virasoro algebra (famous in string theory) is shown to lead to the KdV equation; and in a limiting case, to the Burgers equation for shocks. A hamiltonian formalism for two-dimensional Euler equations is then developed in detail. A discretization of these equations (using a spectral method) is then developed using mathematical ideas from quantum mechanics. Then a hamiltonian formalism for the full three-dimensional Euler equations is developed. The Clebsch variables which provide canonical pairs for fluid dynamics are then explained, in analogy to angular momentum.

HIGHER ORDER BURGERS EQUATION

1986 ◽  
Vol 6 (3) ◽  
pp. 353-360 ◽  
Author(s):  
Mingliang Wang
Keyword(s):  
Burgers Equation ◽  
Higher Order
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