@misc{HussinKiselevKrutovetal.2010, author = {Hussin, V. and Kiselev, A. V. and Krutov, A.O. and Wolf, Thomas}, title = {N=2 supersymmetric a=4-KdV hierarchy derived via Gardner's deformation of Kaup-Boussinesq equation}, issn = {1438-0064}, doi = {10.1063/1.3447731}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11787}, number = {10-16}, year = {2010}, abstract = {We consider the problem of constructing Gardner's deformations for the \$N{=}2\$ supersymmetric \$a{=}4\$--\/Korteweg\/--\/de Vries equation; such deformations yield recurrence relations between the super\/-\/Hamiltonians of the hierarchy. We prove the non\/-\/existence \%P.~Mathieu's Open problem on constructing for of supersymmetry\/-\/invariant \%Gardner's deformations that \%solutions, retract to Gardner's formulas for the KdV equation \%whenever it is assumed that, under the \%respective component reduction. \% in the \$N{=}2\$ super\/-\/field. the solutions . At the same time, we propose a two\/-\/step scheme for the recursive production of the integrals of motion for the \$N{=}2\$,\ \$a{=}4\$--\/SKdV. First, we find a new Gardner's deformation of the Kaup\/--\/Boussinesq equation, which is contained in the bosonic limit of the super\/-\/\%\$N{=}2\$,\ \$a{=}4\$--\/SKdV hierarchy. This yields the recurrence relation between the Hamiltonians of the limit, whence we determine the bosonic super\/- /Hamiltonians of the full \$N{=}2\$, \$a{=}4\$--\/SKdV hierarchy.}, language = {en} }