Boundary Conditions for Multidimensional Integrable Equations

I. T. Habibullin ; E. V. Gudkova

Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 2, pp. 71-83.

Résumé

We suggest an efficient method for finding boundary conditions compatible with integrability for multidimensional integrable equations of Kadomtsev–Petviashvili type. It is observed in all known examples that imposing an integrable boundary condition at a point results in an additional involution for the $t$-operator of the Lax pair. The converse is also likely to be true: if constraints imposed on the coefficients of the $t$-operator of the $L$-$A$ pair result in a broader group of involutions of the $t$-operator, then these constraints determine integrable boundary conditions. New examples of boundary conditions are found for the Kadomtsev–Petviashvili and modified Kadomtsev–Petviashvili equations.

Détail

Keywords: integrable equation, Hamiltonian structure, Kadomtsev–Petviashvili equation
Mots-clés : Lax pair.

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