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Chen, H. H.; Lin, J. E.

On the integrability of multidimensional nonlinear evolution equations. (English) Zbl 0663.35066

J. Math. Phys. 28, 347-350 (1987).
The integrability-test scheme of [H. H. Chen, Y. C. Lee, and C. S. Liu, Phys. Scr. 20, 490-492 (1979)] from one-space dimension to multispace dimensions is generalized. The temporal equation of the Lax pair is still the linearized perturbed equation that defines the symmetries. But the spectral operator in the Lax pair is no longer the linear recursion operator for symmetries. The absence of the linear recursion operator for symmetries in higher spatial dimensions therefore presents no direct obstacle to the Chen-Lee-Liu test scheme. The Kadomtsev-Petviashvili equation is shown as an example.

Cited in 5 Documents

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)

Keywords:

multidimensional nonlinear evolution equations; integrability-test scheme; temporal equation of the Lax pair; linearized perturbed equation; Kadomtsev-Petviashvili equation
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References:

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