Propagation of the Invariance of Germs of Solutions of Quasilinear Differential Equations with Weighted Derivatives
Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 135-143.

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The paper contains various theorems on the propagation of the invariance of germs of solutions for the class of quasilinear differential equations. This class contains model equations of nonlinear waves propagation: the nonlinear Schrödinger equation, the Korteweg–de Vries equation, and some others.
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N. A. Shananin. Propagation of the Invariance of Germs of Solutions of Quasilinear Differential Equations with Weighted Derivatives. Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 135-143. http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a12/

[1] Petrovskii I. G., Ob analitichnosti reshenii sistem uravnenii s chastnymi proizvodnymi. Izbrannye trudy. Sistemy uravnenii s chastnymi proizvodnymi. Algebraicheskaya geometriya, Nauka, M., 1986 | Zbl

[2] Vainberg M. M., Variatsionnye metody issledovaniya nelineinykh operatorov, M., 1956

[3] Calderón A. P., “Uniqueness in Cauchy problem for partial differential equations”, Amer. J. Math., 80 (1958), 16–36 | DOI | MR | Zbl

[4] Shananin N. A., “Ob odnoznachnom prodolzhenii reshenii differentsialnykh uravnenii so vzveshennymi proizvodnymi”, Matem. sb., 191:3 (2000), 113–142 | MR | Zbl

[5] Shananin N. A., “O chastichnoi kvazianalitichnosti obobschennykh reshenii slabo nelineinykh differentsialnykh uravnenii so vzveshennymi proizvodnymi”, Matem. zametki, 68:4 (2000), 608–619 | MR | Zbl

[6] Khermander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, T. 1–4, Mir, M., 1987

[7] Olver P., Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | Zbl

[8] Vinogradov A. M., Krasilschik I. S. i dr., Simmetrii i zakony sokhraneniya uravnenii matematicheskoi fiziki, Nauka, M., 1997