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Weak Concentration And Wave Operator For A 3d Coupled Nonlinear Schrödinger System
Registro en:
Journal Of Mathematical Physics. American Institute Of Physics Inc., v. 56, n. 2, p. - , 2015.
222488
10.1063/1.4908555
2-s2.0-84923599276
Autor
Pastor A.
Institución
Resumen
Reported in this paper are results concerning the Cauchy problem and the dynamics for a cubic nonlinear Schrödinger system arising in nonlinear optics. A sharp criterion is given concerned with the dichotomy global existence versus finite time blow-up. When a radial solution blows up in finite time, we prove the concentration in the critical Lebesgue space. Sufficient condition for the scattering and the construction of the wave operator in the energy space is also provided. 56 2
Agrawal, G.P., (1995) Nonlinear Fiber Optics, , (Academic Press, New York) Bégout, P., Necessary conditions and sufficient conditions for global existence in the nonlinear Schrödinger equation (2002) Adv. Math. Sci. Appl., 12, pp. 817-827 Bergh, J., Löfsröm, J., (1976) Interpolation Spaces: An introduction, , (Springer-Verlag, New York) Cassano, B., Tarulli, M., Cazenave, T., (2003) Semilinear Schrödinger Equations, , (Courant Lectures Notes Vol. 10 (American Mathematical Society, Providence) Chen, J., Guo, B., Blow-up profile to the solutions of two-coupled Schrödinger equations (2009) J. Math. Phys., 50, p. 023505 Christ, F.M., Weinstein, M.I., Dispersion and small amplitude solutions of the generalized Korteweg-de Vries equation (1991) J. Funct. Anal., 100, pp. 87-109 Fanelli, L., Montefusco, E., On the blow-up threshold for weakly coupled nonlinear Schrödinger equations (2007) J. Phys. A: Math. Theor., 40, pp. 14139-14150 Friedman, A., (1969) Partial Differential Equations, , (Holt, Rinehart and Winston, New York) Holmer, J., Roudenko, S., A sharp condition for scattering of the radial 3D nonlinear Schrödinger equation (2008) Commun. Math. Phys., 282, pp. 435-467 Holmer, J., Roudenko, S., On blow-up solutions to the 3D cubic nonlinear Schrödinger equation Appl. Math. Res. Express. Kavian, O., A remark on the blowing-up of solutions to the Cauchy problem for nonlinear Schrödinger equations (1987) Trans. Am. Math. Soc., 299, pp. 193-203 Kenig, C.E., Merle, F., Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case (2006) Invent. Math., 166, pp. 645-675 Kenig, C.E., Ponce, G., Vega, L., Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle (1993) Commun. Pure Appl. Math., 46, pp. 527-620 Killip, R., Visan, M., The radial defocusing energy-supercritical nonlinear wave equation in all sapce dimensions (2011) Proc. Am. Math. Soc., 139, pp. 1805-1817 Li, X., Wu, Y., Lai, S., A sharp threshold of blow-up for coupled nonlinear Schrödinger equations (2010) J. Phys. A: Math. Theor., 43, p. 165205 Lü, Z., Liu, Z., (2011) J. Math. Anal. Appl., 380, pp. 531-539 Ma, L., Zhao, L., Sharp thresholds of blow-up and global existence for the coupled nonlinear Schrödinger system (2008) J. Math. Phys., 49, p. 062103 Maia, L.A., Montefusco, E., Pellacci, B., Positive solutions for a weakly coupled nonlinear Schrödinger system (2006) J. Differ. Equations, 229, pp. 743-767 Merle, F., Tsutsumi, Y., (1990) J. Differ. Equations, 84, pp. 205-214 Sz Nagy, B.V., über Integralgleichungen zwischen einer Funktion und ihrer Ableitung (1941) Acta Univ. Szeged. Sect. Sci. Math., 10, pp. 64-74 Nguyen, N.V., Tian, R., Deconinck, B., Sheils, N., Global existence for a coupled system of Schrödinger equations with power-type nonlinearities (2013) J. Math. Phys., 54, p. 011503 Ogawa, T., Tsutsumi, Y., Blow-up of (1991) J. Differ. Equations, 92, pp. 317-330 Prytula, V., Vekslerchik, V., Pérez-García, V.M., Collapse in coupled nonlinear Schrödinger equations: Sufficient conditions and applications (2009) Physica D, 238, pp. 1462-1467 Song, X., Sharp thresholds of global existence and blowup for a system of Schrödinger equations with combined power-type nonlinearities (2010) J. Math. Phys., 51, p. 033509 Strauss, W., Nonlinear scattering theory at low energy (1981) J. Funct. Anal., 41, pp. 110-133 Strauss, W., (1989) Nonlinear Wave Equations, , (CBMS Regional Conference Series in Mathematics Vol. 73 (American Mathematical Society, Providence) Strauss, W., Existence of solitary waves in higher dimensions (1977) Commun. Math. Phys., 55, pp. 149-162 Weinstein, M.I., Nonlinear Schrödinger equations and sharp interpolation estimates (1983) Commun. Math. Phys., 87, pp. 567-576