Orbital Stability Of Periodic Traveling-wave Solutions For The Regularized Schamel Equation

dc.date2016
dc.date2016-06-03T20:14:05Z
dc.date2016-06-03T20:14:05Z
dc.date.accessioned2018-03-29T01:33:02Z
dc.date.available2018-03-29T01:33:02Z
dc.identifier
dc.identifierPhysica D: Nonlinear Phenomena. Elsevier, v. 317, p. 43 - 58, 2016.
dc.identifier1672789
dc.identifier10.1016/j.physd.2015.12.002
dc.identifierhttp://www.scopus.com/inward/record.url?eid=2-s2.0-84955585451&partnerID=40&md5=bf21a0f0e3566f9825706dfc3875322a
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/238169
dc.identifier2-s2.0-84955585451
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1304830
dc.descriptionIn this work we study the orbital stability of periodic traveling-wave solutions for dispersive models. The study of traveling waves started in the mid-18th century when John S. Russel established that the flow of water waves in a shallow channel has constant evolution. In recent years, the general strategy to obtain orbital stability consists in proving that the traveling wave in question minimizes a conserved functional restricted to a certain manifold. Although our method can be applied to other models, we deal with the regularized Schamel equation, which contains a fractional nonlinear term. We obtain a smooth curve of periodic traveling-wave solutions depending on the Jacobian elliptic functions and prove that such solutions are orbitally stable in the energy space. In our context, instead of minimizing the augmented Hamiltonian in the natural codimension two manifold, we minimize it in a "new" manifold, which is suitable to our purposes. © 2015 Elsevier B.V. All rights reserved.
dc.description317
dc.description
dc.description43
dc.description58
dc.descriptionAngulo, J., Cardoso, E., Natali, F., Stability Properties of Periodic Traveling Waves for the Intermediate Long Wave Equation, , arxiv:1503.04350
dc.descriptionDe Andrade, T.P., Pastor, A., Nonlinear Stability of Periodic Waves for Modified Korteweg-de Vries and Gardner Equations, , (in preparation)
dc.descriptionBenjamin, T.B., Bona, J.L., Mahony, J.J., Model equations for long waves in nonlinear dispersive systems (1972) Phil. Trans. R. Soc., 272, pp. 47-78
dc.descriptionSchamel, H., Stationary solitary, Snoidal and Sinusoidal ion acoustic waves (1972) Plasma Phys., 14, pp. 905-924
dc.descriptionSchamel, H., A modified Korteweg-de Vries equation for ion acoustic waves due to resonant electrons (1973) J. Plasma Phys., 9, pp. 377-387
dc.descriptionBroer, L.J.F., Sluijter, F.W., Stable approximate equations for ion-acoustic waves (1977) Phys. Fluids, 20, pp. 1458-1460
dc.descriptionTran, M.Q., Ion acoustic solitons in a plasma: A review of their experimental properties and related theories (1979) Phys. Scr., 20, pp. 317-327
dc.descriptionBroer, L.J.F., Van Groesen, E.W.C., Timmers, J.M.W., Stable model equations for long water waves (1976) Appl. Sci. Res., 32, pp. 619-636
dc.descriptionGill, T.S., Bedi, C., Saini, N.S., Higher order nonlinear effects on wave structures in a four-component dusty plasma with nonisothermal electrons (2011) Phys. Plasmas, 18
dc.descriptionBronski, J.C., Johnson, M.A., Kapitula, T., An index theorem for the stability of periodic travelling waves of Korteweg-de Vries type (2011) Proc. Roy. Soc. Edinburgh Sect. A, 141, pp. 1141-1173
dc.descriptionSouganidis, P.E., Strauss, W.A., Instability of a class of dispersive solitary waves (1990) Proc. Roy. Soc. Edinburgh Sect. A, 114, pp. 195-212
dc.descriptionBona, J.L., McKinney, W.R., Restrepo, J.M., Stable and unstable solitary-wave solutions of the generalized regularized long-wave equation (2000) J. Nonlinear Sci., 10, pp. 603-638
dc.descriptionJohnson, M.A., On the stability of periodic solutions of the generalized Benjamin-Bona-Mahony equation (2010) Physica D, 239, pp. 1892-1908
dc.descriptionLin, Z., Instability of nonlinear dispersive solitary waves (2008) J. Funct. Anal., 255, pp. 1191-1224
dc.descriptionBenjamin, T.B., The stability of solitary waves (1972) Proc. R. Soc., 328, pp. 153-183
dc.descriptionGrillakis, M., Shatah, M., Strauss, W., Stability theory of solitary waves in the presence of symmetry i (1987) J. Funct. Anal., 74, pp. 160-197
dc.descriptionWeinstein, M.I., Lyapunov stability of ground states of nonlinear dispersive evolution equations (1986) Comm. Pure Appl. Math., 39, pp. 51-67
dc.descriptionWeinstein, M.I., Existence and dynamic stability of solitary wave solutions of equations arising in long wave propagation (1987) Comm. Partial Differential Equations, 12, pp. 1133-1173
dc.descriptionAlvarez, B., Angulo, J., Existence and stability of periodic travelling-wave solutions of the Benjamin equation (2005) Commun. Pure Appl. Anal., 4, pp. 367-388
dc.descriptionAngulo, J., Natali, F., Stability and instability of periodic travelling waves solutions for the critical Korteweg-de Vries and non-linear Schrödinger equations (2009) Physica D, 238, pp. 603-621
dc.descriptionAngulo, J., (2009) Nonlinear Dispersive Equations: Existence and Stability of Solitary and Periodic Travelling Wave Solutions, 156. , Math. Surveys Monogr. American Mathematical Society
dc.descriptionAngulo, J., Pastor, A., Stability of periodic optical solitons for a nonlinear Schrödinger system (2009) Proc. Roy. Soc. Edinburgh Sect. A, 139, pp. 927-959
dc.descriptionAngulo, J., Nonlinear stability of periodic travelling wave solutions to the Schrödinger and modified Korteweg-de Vries equations (2007) J. Differential Equations, 235, pp. 1-30
dc.descriptionAngulo, J., Banquet, C., Scialom, M., Stability for the modified and fourth-order Benjamin-Bona-Mahony equations (2011) Discrete Contin. Dyn. Syst., 30, pp. 851-871
dc.descriptionAngulo, J., Bona, J.L., Scialom, M., Stability of cnoidal waves (2006) Adv. Differential Equations, 11, pp. 1321-1374
dc.descriptionFarah, L.G., Pastor, A., On the periodic Schrödinger-Boussinesq system (2010) J. Math. Anal. Appl., 368, pp. 330-349
dc.descriptionHakkaev, S., Iliev, I.D., Kirchev, K., Stability of periodic traveling waves for complex modified Korteweg-de Vries equation (2010) J. Differential Equations, 248, pp. 2608-2627
dc.descriptionNatali, F., Pastor, A., Stability properties of periodic standing waves for the Klein-Gordon-Schrödinger system (2010) Commun. Pure Appl. Anal., 9, pp. 413-430
dc.descriptionNatali, F., Pastor, A., Stability and instability of periodic standing wave solutions for some Klein-Gordon equations (2008) J. Math. Anal. Appl., 347, pp. 428-441
dc.descriptionNeves, A., Floquet's Theorem and stability of periodic solitary waves (2009) J. Dynam. Differential Equations, 21, pp. 555-565
dc.descriptionJohnson, M.A., Nonlinear stability of periodic traveling wave solutions of the generalized Korteweg-de Vries equation (2009) SIAM J. Math. Anal., 41, pp. 1921-1947
dc.descriptionNatali, F., Neves, A., Orbital stability of periodic waves (2013) IMA J. Appl. Math., 79, pp. 1-19
dc.descriptionByrd, P.F., Friedman, M.D., (1971) Handbook of Elliptic Integrals for Engineers and Scientists, , second ed. Springer NY
dc.descriptionHale, J.K., (1980) Ordinary Differential Equation, , Revised ed. Dover Publications New York
dc.descriptionEastham, M.S.P., (1973) The Spectral Theory of Periodic Differential Equations, , Scottish Academic Press Edinburgh
dc.descriptionInce, E.L., The periodic Lamé functions (1940) Proc. Roy. Soc. Edinburgh, 60, pp. 47-63
dc.descriptionNeves, A., Isoinertial family of operators and convergence of KdV cnoidal waves to solitons (2008) J. Differential Equations, 244, pp. 875-886
dc.descriptionBona, J.L., Souganidis, P.E., Strauss, W.A., Stability and instability of solitary waves of the Korteweg-de Vries type (1987) Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 411, pp. 395-412
dc.description
dc.description
dc.languageen
dc.publisherElsevier
dc.relationPhysica D: Nonlinear Phenomena
dc.rightsfechado
dc.sourceScopus
dc.titleOrbital Stability Of Periodic Traveling-wave Solutions For The Regularized Schamel Equation
dc.typeArtículos de revistas


Este ítem pertenece a la siguiente institución