Geodesic
Simple exact solutions and asymptotic localized solutions of the two-dimensional massless Dirac equation for graphene
Teoretičeskaâ i matematičeskaâ fizika, Tome 196 (2018) no. 1, pp. 64-69 Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct exact solutions and asymptotic localized solutions of the two-dimensional massless Dirac equation for graphene with a small potential.
Keywords: massless Dirac equation for graphene, creation operator.
Mots-clés : exact solution 
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A. A. Tolchennikov. Simple exact solutions and asymptotic localized solutions of the two-dimensional massless Dirac equation for graphene. Teoretičeskaâ i matematičeskaâ fizika, Tome 196 (2018) no. 1, pp. 64-69. http://geodesic.mathdoc.fr/item/TMF_2018_196_1_a5/

[1] S. Yu. Dobrokhotov, S. Ya. Sekerzh-Zenkovich, “Odin klass tochnykh algebraicheskikh lokalizovannykh reshenii mnogomernogo volnovogo uravneniya”, Matem. zametki, 88:6 (2010), 942–945 | DOI | DOI | MR

[2] L. N. Sretenskii, Teoriya volnovykh dvizhenii zhidkosti, Nauka, M., 1977; С. Ф. Доценко, Б. Ю. Сергиевский, Л. В. Черкасов, “Пространственные волны цунами, вызванные знакопеременным смещением поверхности океана”, Исследования цунами, Вып. 1, Междувед. геофиз. ком., М., 1986, 7–14; S. Wang, B. Le Mehaute, C.-C. Lu, “Effect of dispersion on impulsive waves”, Mar. Geophys. Res., 9:2 (1987), 95–111 ; S. Ya. Sekerzh-Zenkovich, “Simple asymptotic solution of the Cauchy–Poisson problem for head waves”, Russ. J. Math. Phys., 16:2 (2009), 315–322 | DOI | DOI | MR

[3] M. I. Katsnelson, Graphene: Carbon in Two Dimensions, Cambridge Univ. Press, New York, 2012

[4] 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. RAN, 464:3 (2015), 261–266 | DOI | DOI

[5] 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

[6] S. A. Sergeev, A. A. Tolchennikov, “Ob ‘operatorakh rozhdeniya’ v zadache o lokalizovannykh resheniyakh linearizovannykh uravnenii melkoi vody s regulyarnymi i osobymi kharakteristikami”, Matem. zametki, 100:6 (2016), 911–922 | DOI | DOI | MR

[7] S. Yu. Dobrokhotov, R. V. Nekrasov, B. Tirozzi, “Asymptotic solutions of the linear shallow-water equations with localized initial data”, J. Eng. Math., 69:2–3 (2011), 225–242 | DOI | MR

[8] S. Yu. Dobrokhotov, A. I. Shafarevich, B. Tirozzi, “Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations”, Russ. J. Math. Phys., 15:2 (2008), 192–221 | DOI | MR