Geodesic
Trace formulas for the one-dimensional Stark operator and integrals of motion for the cylindrical Korteweg-de Vries equation
Algebra i analiz, Tome 31 (2019) no. 5, pp. 206-215.

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

A complete series of trace formulas for the one-dimensional Stark operator on the entire axis with a rapidly decreasing potential is constructed. The Stark equation is related to the cylindrical Korteweg-de Vries equation by the pair ( $ L$–$ A$). For this equation, infinite series of integrals of motion is constructed that corresponds to the trace formulas for the Stark operator.
Keywords: trace formulas, Stark operator, integrals of motion, cylindrical Korteweg–de Vries equation, inverse problem. 
@article{AA_2019_31_5_a6,
     author = {V. V. Sukhanov},
     title = {Trace formulas for the one-dimensional {Stark} operator and integrals of motion for the cylindrical {Korteweg-de} {Vries} equation},
     journal = {Algebra i analiz},
     pages = {206--215},
     publisher = {mathdoc},
     volume = {31},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2019_31_5_a6/}
}
TY  - JOUR
AU  - V. V. Sukhanov
TI  - Trace formulas for the one-dimensional Stark operator and integrals of motion for the cylindrical Korteweg-de Vries equation
JO  - Algebra i analiz
PY  - 2019
SP  - 206
EP  - 215
VL  - 31
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2019_31_5_a6/
LA  - ru
ID  - AA_2019_31_5_a6
ER  - 
%0 Journal Article
%A V. V. Sukhanov
%T Trace formulas for the one-dimensional Stark operator and integrals of motion for the cylindrical Korteweg-de Vries equation
%J Algebra i analiz
%D 2019
%P 206-215
%V 31
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2019_31_5_a6/
%G ru
%F AA_2019_31_5_a6
V. V. Sukhanov. Trace formulas for the one-dimensional Stark operator and integrals of motion for the cylindrical Korteweg-de Vries equation. Algebra i analiz, Tome 31 (2019) no. 5, pp. 206-215. http://geodesic.mathdoc.fr/item/AA_2019_31_5_a6/

[1] Calogero F., Degasperis A., “Inverse spectral problem for the one-dimentional Shröedinger equation with an additional linear potential”, Lett. Nuovo Cimento (2), 23:4 (1978), 143–149 | DOI | MR

[2] Katchalov A. P., Kurylev Ya. V., “Inverse scattering problem for a one-dimensional Stark-effect Hamiltonian”, Inverse Problems, 6:1 (1990), L1–L5 | DOI | MR | Zbl

[3] Korotyaev E., “Resonances for $1$d Stark operators”, J. Spectr. Theory, 7 (2017), 699–732 | DOI | MR | Zbl

[4] Korotyaev E., Asymptotics of resonances for $1$d Stark operators, arXiv: 1705.08072 [math-ph] | MR

[5] Korotyaev E., Pushnitski A., “Trace formulae and high energy asymptotics for the Stark operator”, Comm. Partial Differential Equations, 28:3 (2003), 817–842 | DOI | MR | Zbl

[6] Buslaev V. S., Faddeev L. D., “O formulakh sledov dlya differentsialnogo singulyarnogo operatora tipa Shturma–Liuvillya”, Dokl. AN SSSR, 132:1 (1960), 13–16 | Zbl

[7] Its A. R., Sukhanov V., “Riemann–Hilbert approach to the inverse problem for Stark equation on the line”, Inverse Problems, 32:5 (2016), 055003 | DOI | MR | Zbl

[8] Calogero F., Degasperis A., “Solution by the spectral-transform method of a nonlinear evolution equation, including as a special case the cylindrical KdV equation”, Lett. Nuovo Cimento (2), 23:4 (1978), 150–154 | DOI | MR

[9] Abramowitz M., Stegun I. A., Handbook of mathematical functions with formulas, graphs and mathematical tables, National Bureau Standards Appl. Math. Ser., 55, Dover Publ., Washington, DC, 1964 | MR