Geodesic
Boundary Conditions for Multidimensional Integrable Equations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 2, pp. 71-83

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: integrable equation, Hamiltonian structure, Kadomtsev–Petviashvili equation
Mots-clés : Lax pair. 
@article{FAA_2004_38_2_a6,
     author = {I. T. Habibullin and E. V. Gudkova},
     title = {Boundary {Conditions} for {Multidimensional} {Integrable} {Equations}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {71--83},
     publisher = {mathdoc},
     volume = {38},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2004_38_2_a6/}
}
TY  - JOUR
AU  - I. T. Habibullin
AU  - E. V. Gudkova
TI  - Boundary Conditions for Multidimensional Integrable Equations
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2004
SP  - 71
EP  - 83
VL  - 38
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2004_38_2_a6/
LA  - ru
ID  - FAA_2004_38_2_a6
ER  - 
%0 Journal Article
%A I. T. Habibullin
%A E. V. Gudkova
%T Boundary Conditions for Multidimensional Integrable Equations
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2004
%P 71-83
%V 38
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2004_38_2_a6/
%G ru
%F FAA_2004_38_2_a6
I. T. Habibullin; E. V. Gudkova. Boundary Conditions for Multidimensional Integrable Equations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 2, pp. 71-83. http://geodesic.mathdoc.fr/item/FAA_2004_38_2_a6/