Geodesic
Behavior of the solution of the Klein–Gordon equation with a localized initial condition
Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 2, pp. 330-340 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the Klein–Gordon equation with a localized initial condition and describe the transition of the solution from localized to rapidly oscillating when the equation parameter changes.
Mots-clés : Klein–Gordon equation
Keywords: localized initial condition. 
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A. A. Tolchennikov. Behavior of the solution of the Klein–Gordon equation with a localized initial condition. Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 2, pp. 330-340. http://geodesic.mathdoc.fr/item/TMF_2019_199_2_a10/

[1] S. Yu. Dobrokhotov, P. N. Zhevandrov, V. P. Maslov, A. I. Shafarevich, “Asimptoticheskie bystroubyvayuschie resheniya lineinykh strogo giperbolicheskikh sistem s peremennymi koeffitsientami”, Matem. zametki, 49:4 (1991), 31–46 | DOI | MR | Zbl

[2] A. I. Allilueva, S. Yu. Dobrokhotov, S. A. Sergeev, A. I. Shafarevich, “Novye predstavleniya kanonicheskogo operatora Maslova i lokalizovannye asimptoticheskie resheniya strogo giperbolicheskikh sistem”, Dokl. AN, 464:3 (2015), 261–266 | DOI | MR | Zbl

[3] S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Prokolotye lagranzhevy mnogoobraziya i asimptoticheskie resheniya lineinykh uravnenii voln na vode s lokalizovannymi nachalnymi usloviyami”, Matem. zametki, 101:6 (2017), 936–943 | DOI | DOI | MR

[4] S. Yu. Dobrokhotov, S. Ya. Sekerzh-Zen'kovich, A. A. Tolchennikov, “Exact and asymptotic solutions of the Cauchy–Poisson problem with localized initial conditions and a constant function of the bottom”, Russ. J. Math. Phys., 24:3 (2017), 310–321 | DOI | MR

[5] S. Yu. Dobrokhotov, S. A. Sergeev, B. Tirozzi, “Asymptotic solutions of the Cauchy problem with localized initial conditions for linearized two-dimensional Boussinesq-type equations with variable coefficients”, Russ. J. Math. Phys., 20:2 (2013), 155–171 | DOI | MR

[6] S. A. Sergeev, “Asimptoticheskie resheniya odnomernogo linearizovannogo uravneniya Kortevega–de Friza s lokalizovannymi nachalnymi dannymi”, Matem. zametki, 102:3 (2017), 445–461 | DOI | DOI | MR

[7] S. A. Sergeev, “Asimptoticheskie resheniya odnomernogo lineinogo evolyutsionnogo uravneniya dlya poverkhnostnykh voln s uchetom poverkhnostnogo natyazheniya”, Matem. zametki, 103:3 (2018), 475–480 | DOI | DOI

[8] G. Bete, Kvantovaya mekhanika, Mir, M., 1965 | MR

[9] S. Yu. Dobrokhotov, B. Tirozzi, A. A. Tolchennikov, “Asymptotics of shallow water equations on the sphere”, Russ. J. Math. Phys., 21:4 (2014), 430–449 | DOI | MR

[10] I. Bryuning, S. Yu. Dobrokhotov, M. I. Katsnelson, D. S. Minenkov, “Kvaziklassicheskie asimptotiki i plotnost sostoyanii dlya dvumernykh tsentralno-simmetrichnykh uravnenii Shredingera i Diraka v zadachakh tunnelnoi mikroskopii”, TMF, 186:3 (2016), 386–400 | DOI | DOI | MR

[11] V. V. Kucherenko, “Asimptotika resheniya sistemy $A(x,-ih\frac\partial{\partial x})$ pri $h\to0$ v sluchae kharakteristik peremennoi kratnosti”, Izv. AN SSSR. Ser. matem., 38:3 (1974), 625–662 | DOI | MR | Zbl

[12] M. V. Fedoryuk, Asimptotika. Integraly i ryady, Nauka, M., 1987 | MR