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Results tagged with integrable-systems
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user 106467
9
votes
Proving a system is nonintegrable /not solvable with Inverse Scattering Transform
The prolongation structure method developed by Wahlquist and Estabrook is one method to show whether or not a PDE is solvable via the inverse scattering transform. (There are others - refer Y. Kosman …
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2
votes
References for infinite-dimensional integrable systems?
It's not entirely clear what you mean by a "physical/geometric understanding of the corresponding integrable system" because each one will be unique in some sense.
A good collection of survey papers …
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2
votes
What functions do we need to solve linear second order differential equations with polynomia...
For an account of integrability of linear ODE in the way that you describe, refer section 4 of the 2004 paper
A.G. Khovanskii, "On solvability and unsolvability of equations in explicit form"
Uspekhi …
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2
votes
Accepted
Lax pair of an integrable non-linear PDE
You could try using the Wahlquist-Estabrook prolongation structure technique, per H.D. Wahlquist and F.B. Estabrook, J. Math. Phys 16 (1975) 1-7 (covering the Korteweg-deVries equation), & F.B. Estabr …
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1
vote
Literature on ZS-AKNS systems with independent potentials
Beals and Coifman provided a general analysis of the IST for the $N\times N$ version of the AKNS problem (see Comm. Pure Appl. Math. 37 (1984) 39-90 and their subsequent papers).
Their analysis appea …
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1
vote
Integrability conditions for differential equations on $J^\infty$
Section 4 of the paper "Geometry of Differential Equations" by B. Kruglikov and V. Lychagin (IHES/M/07/04) states that formal integrability & analyticity are sufficient for the existence of a solution …
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1
vote
Lax pairs in an abstract formalism
The paper by R. Beals and R. R. Coifman, "Inverse Scattering and Evolution Equations" Communications on Pure and Applied Mathematics 38(1) (1985) pp. 29-42 may be helpful.
They do go beyond the KdV eq …
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