A SYMMETRY APPROACH TO EXACTLY SOLVABLE EVOLUTION EQUATIONS

1980
8 pages
Published in:
  • J.Math.Phys. 21 (1980) 1318-1325

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Abstract: (AIP)
A method is developed for establishing the exact solvability of nonlinear evolution equations in one space dimension which are linear with constant coefficient in the highest‐order derivative. The method, based on the symmetry structure of the equations, is applied to second‐order equations and then to third‐order equations which do not contain a second‐order derivative. In those cases the most general exactly solvable nonlinear equations turn out to be the Burgers equation and a new third‐order evolution equation which contains the Korteweg‐de Vries (KdV) equation and the modified KdV equation as particular cases.
  • FIELD EQUATIONS: NONLINEAR
  • Korteweg-de Vries equation
  • FIELD EQUATIONS: SOLUTION
  • TRANSFORMATION: BAECKLUND
  • FIELD THEORY: COMMUTATION RELATIONS
  • MATHEMATICAL METHODS
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