Geodesic
Construction of periodic solutions of a Boussinnesq type equation using the method of quasi-normal forms
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 1, pp. 207-220 
A. Yu. Kolesov; N. Kh. Rozov. Construction of periodic solutions of a Boussinnesq type equation using the method of quasi-normal forms. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 1, pp. 207-220. http://geodesic.mathdoc.fr/item/FPM_1995_1_1_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Using the asymptotic method of quasi-normal forms the dynamic characteristics of the following boundary value problem are analyzed: $$ \begin{array}{c} u_{tt}-u_{xx}-\varepsilon a^2 u_{xxtt} =\varepsilon\alpha u_{xxt}+\varepsilon u_{t}-u^2u_{t}, \\[2mm] \left.u\right|_{x=0}=\left.u\right|_{x=1}=0,\quad \alpha=\mathrm{const}>0,\quad 0\varepsilon\ll1. \end{array} $$

[1] A. Yu. Kolesov, “Ustoichivost avtokolebanii telegrafnogo uravneniya, bifurtsiruyuschikh iz sostoyaniya ravnovesiya”, Mat. zametki, 51:2 (1992), 59–65 | MR | Zbl

[2] Nelineinye volny, eds. S. Leibovicha i A. Sibassa, Mir, M., 1977 | MR

[3] Yu. S. Kolesov, “Metod kvazinormalnykh form v zadache ob ustanovivshikhsya rezhimakh parabolicheskikh sistem s maloi diffuziei”, Ukr. mat. zhurn., 39:1 (1987), 28–34 | MR | Zbl

[4] Yu. S. Kolesov, “Bifurkatsiya invariantnykh torov parabolicheskikh sistem s maloi diffuziei”, Mat. sb., 184:3 (1993), 121–136 | MR | Zbl

[5] A. Yu. Kolesov, “Avtokolebaniya singulyarno vozmuschennykh parabolicheskikh sistem pervoi stepeni negrubosti”, Mat. zametki, 49:5 (1991), 62–69 | MR | Zbl

[6] Yu. S. Kolesov, “Ob ustoichivosti reshenii lineinykh differentsialnykh uravnenii parabolicheskogo tipa s pochti periodicheskimi koeffitsientami”, Tr. Mosk. mat. obsch-va, 36 (1978), 3–27 | MR | Zbl

[7] Yu. S. Kolesov, V. V. Maiorov, “Novyi metod issledovaniya ustoichivosti reshenii lineinykh differentsialnykh uravnenii s blizkimi k postoyannym pochti periodicheskimi koeffitsientami”, Differents. uravneniya, 10 (1974), 1778–1787 | MR