On exact solutions of a nonclassical partial differential equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 11, pp. 1870-1875 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a nonclassical nonlinear partial differential equation, several classes of solutions expressed in terms of elementary and special functions are constructed. Moreover, solutions of one of the classes contain an arbitrary sufficiently smooth function of a single argument. It is shown that, among these solutions, there are ones going to infinity in a finite time (blowing up) and ones that are bounded on any finite time interval.
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A. I. Aristov. On exact solutions of a nonclassical partial differential equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 11, pp. 1870-1875. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_11_a5/

[1] Rabinovich M. I., Trubetskov D. I., Vvedenie v teoriyu kolebanii i voln, Nauka, M., 1984

[2] Rabinovich M. I., “Avtokolebaniya raspredelennykh sistem”, Izvestiya vuzov. Radiofiz., 17:4 (1974), 477–510

[3] Korpusov M. O., Razrushenie v neklassicheskikh volnovykh uravneniyakh, URSS, M., 2010

[4] Zaitsev V. F., Polyanin A. D., Spravochnik po nelineinym differentsialnym uravneniyam, Fizmatlit, M., 1993 | MR

[5] Polyanin A. D., Zaitsev V. F., Zhurov A. I., Metody resheniya nelineinykh uravnenii matematicheskoi fiziki i mekhaniki, Fizmatlit, M., 2005

[6] Alshin A. B., Korpusov M. O., Yushkov E. V., “Beguschaya volna kak reshenie nelineinogo uravneniya v poluprovodnikakh s silnoi prostranstvennoi dispersiei”, Zh. vychisl. matem. i matem. fiz., 48:5 (2008), 808–812 | MR | Zbl

[7] Ibragimov N. Kh., Prakticheskii kurs differentsialnykh uravnenii i matematicheskogo modelirovaniya, Fizmatlit, M., 2012