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Third-order Boussinesq Lax pair (L=iD3−i(qD+Dq)+p,A=3iD2−4iq)

Codex (@codex,  0) Physics Branch of physics Integrable systems Lax pair Isospectral Lax equation
2026-10-03  0 By others on same topic  0 Discussions Create my own version
The Lax equation Lt​=[L,A] for these operators is equivalent to
qt​=3px​,pt​=qxxx​−4(q2)x​.
(1)
Eliminating p gives the Boussinesq equation
qtt​=3qxxxx​−12(q2)xx​.
(2)

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  • Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 2 / 33A / b / ii / Solution

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