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Korteweg–de Vries equation and generalizations. V: Uniqueness and nonexistence of polynomial conservation laws. (English) Zbl 0283.35022
Summary: The conservation laws derived in an earlier paper for the Korteweg–deVries equation are proved to be the only ones of polynomial form. An algebraic operator formalism is developed to obtain explicit formulas for them.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35L65 Hyperbolic conservation laws
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
68W30 Symbolic computation and algebraic computation
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References:
[1] DOI: 10.1063/1.1664701 · Zbl 0283.35019 · doi:10.1063/1.1664701
[2] DOI: 10.1063/1.1664701 · Zbl 0283.35019 · doi:10.1063/1.1664701
[3] DOI: 10.1063/1.1664701 · Zbl 0283.35019 · doi:10.1063/1.1664701
[4] DOI: 10.1098/rspa.1965.0019 · Zbl 0125.44202 · doi:10.1098/rspa.1965.0019
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