Multidimensional integrable boundary problems
I. T. Habibullin
Abstract
A method of looking for boundary conditions consistent with the integrability property of multidimensional Kadomtsev-Petviashvili (KP) type equations is discussed. The method is based on involutions of the Lax pair taken at the border plane. New classes of boundary conditions for the KP and Hirota equations are proposed consistent with the Lax pair. The boundary problem on the stripe 0<y<1 for the KP equation is discussed, its exact solutions are found. Ward's problem on discrete versions of the generalized Toda chains is briefly discussed.
Create a lesson
Related papers
Integrability of the deformed Toda systems
Mikhail Vasilev
An integrable Z22-graded extension of Camassa-Holm equation and its bi-Hamiltonian structure
N. Aizawa, Ichi Fujii, Ren Ito et al.
Maxwell's relations as Hamilton's equations: a symplectic and variational framework
Sikarin Yoo-Kong
The Nakamura Conjecture Revisited: Toda Molecules and Stationary Axisymmetric Gravity
Takeshi Fukuyama
Multivariable Painleve'-II equation: connection formulas for arbitrary system size
Nikolai A. Sinitsyn
Vector rogue wave patterns associated with generalized Hermite and Okamoto polynomials
Hejiaqi Chen, Dongwei Wu, Chengfa Wu et al.