Abstract:
In the generic position case properties of the variations of scattering data are studied
for a smooth fast decreasing potential of the Sturm–Liouville problem. Orthogonality
and completeness relations for bilinear combinations of the lost solutions
of this problem are formulated in a more precise form and properties of the recursion
operator and its resolvent are thoroughly analysed.
Citation:
V. A. Arkad'ev, A. K. Pogrebkov, M. K. Polivanov, “Expansions with respect to squares, symplectic and poisson structures associated with the Sturm–Liouville problem. I”, TMF, 72:3 (1987), 323–339; Theoret. and Math. Phys., 72:3 (1987), 909–920
This publication is cited in the following 11 articles:
Dianlou Du, Xue Wang, “A new finite-dimensional Hamiltonian systems with a mixed Poisson structure for the KdV equation”, Theoret. and Math. Phys., 211:3 (2022), 745–757
Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov, “On the integrability of KdV hierarchy with self-consistent sources”, CPAA, 11:4 (2012), 1439
V.S. Gerdjikov, G. Vilasi, A.B. Yanovski, Lecture Notes in Physics, 748, Integrable Hamiltonian Hierarchies, 2008, 37
Adrian Constantin, Vladimir S Gerdjikov, Rossen I Ivanov, “Generalized Fourier transform for the Camassa–Holm hierarchy”, Inverse Problems, 23:4 (2007), 1565
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L. A. Kalyakin, “Asymptotics of the first correction in the perturbation of the NN-soliton solution to the KdV equation”, Math. Notes, 58:2 (1995), 814–823
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M. Boiti, L. Martina, F. Pempinelli, “Multidimensional localized solitons”, Chaos, Solitons & Fractals, 5:12 (1995), 2377
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S. V. Talalov, “Spinning string in four-dimensional spacetime as a model of SL(2,C) chiral field with anomaly. II”, Theoret. and Math. Phys., 83:1 (1990), 377–382
V. A. Arkad'ev, A. K. Pogrebkov, M. K. Polivanov, “Expansions with respect to squares, symplectic and poisson structures associated with the Sturm–Liouville problem. II”, Theoret. and Math. Phys., 75:2 (1988), 448–460
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