Abstract:
A Sturm–Liouville problem on compact graphs is formulated and
analyzed. The scattering problem for the Schrödinger equation on
noncompact graphs is also formulated and analyzed.
Citation:
N. I. Gerasimenko, B. S. Pavlov, “Scattering problems on noncompact graphs”, TMF, 74:3 (1988), 345–359; Theoret. and Math. Phys., 74:3 (1988), 230–240
This publication is cited in the following 105 articles:
Sergei Avdonin, Nina Avdonina, Olha Sus, “Inverse dynamic problem for the Dirac system on finite metric graphs and the leaf peeling method”, J. Phys. A: Math. Theor., 58:5 (2025), 055203
Pavel Kurasov, Operator Theory: Advances and Applications, 293, Spectral Geometry of Graphs, 2024, 1
Francesco Demontis, Cornelis van der Mee, “From the AKNS system to the matrix Schrödinger equation with vanishing potentials: Direct and inverse problems”, Stud Appl Math, 150:2 (2023), 481
Serifenur Cebesoy, Elgiz Bairamov, Yelda Aygar, “Scattering problems of impulsive Schrödinger equations with matrix coefficients”, Ricerche mat, 72:1 (2023), 399
Gaukhar Arepova, Ludmila Alexeyeva, Dana Arepova, “Solution to the Dirichlet Problem of the Wave Equation on a Star Graph”, Mathematics, 11:20 (2023), 4234
Francesco Demontis, Cornelis van der Mee, “A Matrix Schrödinger Approach to Focusing Nonlinear Schrödinger Equations with Nonvanishing Boundary Conditions”, J Nonlinear Sci, 32:4 (2022)
Yaroslav Granovskyi, Mark Malamud, Hagen Neidhardt, “Non-compact Quantum Graphs with Summable Matrix Potentials”, Ann. Henri Poincaré, 22:1 (2021), 1
Pavel Kurasov, Jacob Muller, “n-Laplacians on Metric Graphs and Almost Periodic Functions: I”, Ann. Henri Poincaré, 22:1 (2021), 121
D S Nikiforov, I V Blinova, I Y Popov, “Schrödinger and Dirac dynamics on time-dependent quantum graph”, Indian J Phys, 93:7 (2019), 913
Kiyoshi Mochizuki, Igor Trooshin, Trends in Mathematics, Analysis, Probability, Applications, and Computation, 2019, 199
Anton I. Popov, Igor Y. Popov, Dmitri S. Nikiforov, Irina V. Blinova, CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST), 2133, CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST), 2019, 290007
Kirill Cherednichenko, Yulia Ershova, Alexander V. Kiselev, “Time-Dispersive Behavior as a Feature of Critical-Contrast Media”, SIAM J. Appl. Math., 79:2 (2019), 690
Jan Boman, Pavel Kurasov, Rune Suhr, “Schrödinger Operators on Graphs and Geometry II. Spectral Estimates for \varvecL1\varvecL1 L 1 -potentials and an Ambartsumian Theorem”, Integr. Equ. Oper. Theory, 90:3 (2018)
Igor Y. Popov, Dmitri S. Nikiforov, “Classical and quantum wave dynamics on time-dependent geometric graph”, Chinese Journal of Physics, 56:2 (2018), 747
Kiyoshi Mochizuki, Igor Trooshin, Trends in Mathematics, New Trends in Analysis and Interdisciplinary Applications, 2017, 319
Ricardo Weder, “The number of eigenvalues of the matrix Schrödinger operator on the half line with general boundary conditions”, Journal of Mathematical Physics, 58:10 (2017)
Efendiev R.F. Orudzhev H.D. El-Raheem Z.F., “Spectral analysis of wave propagation on branching strings”, Bound. Value Probl., 2016, 215
Ricardo Weder, “Trace formulas for the matrix Schrödinger operator on the half-line with general boundary conditions”, Journal of Mathematical Physics, 57:11 (2016)
Ricardo Weder, “Scattering theory for the matrix Schrödinger operator on the half line with general boundary conditions”, Journal of Mathematical Physics, 56:9 (2015)
Igor Yu Popov, Irina V Blinova, Anton I Popov, “Discrete spectrum for quantum graph with local disturbance of the periodicity”, J. Phys.: Conf. Ser., 661 (2015), 012024