Quasi-periodic solutions of the \(2+1\) dimensional modified Korteweg-de Vries equation. (English) Zbl 0937.35155

Geng, Xianguo; Cao, Cewen

Phys. Lett., A 261, No. 5-6, 289-296 (1999).

Summary: A new \(2 + 1\) dimensional modified Korteweg-de Vries equation is proposed and decomposed into the first two members of the well-known Kaup-Newell hierarchy, which are reduced further into integrable ordinary differential equations in the invariant set produced by the stationary Kaup-Newell equation. The Abel-Jacobi coordinates are introduced to straighten out the flows, from which quasi-periodic solutions of the \(2 + 1\) dimensional modified Korteweg-de Vries equation are obtained in terms of the Riemann theta functions.

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
35B10	Periodic solutions to PDEs
37K20	Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions

Keywords:

modified Korteweg-de Vries equation; Kaup-Newell hierarchy; quasi-periodic solutions; Riemann theta functions

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