Artículos de revistas
Unique Continuation Property For A Higher Order Nonlinear Schrödinger Equation
Registro en:
Journal Of Mathematical Analysis And Applications. , v. 303, n. 1, p. 188 - 207, 2005.
0022247X
10.1016/j.jmaa.2004.08.030
2-s2.0-12744280564
Autor
Carvajal X.
Panthee M.
Institución
Resumen
We prove that, if a sufficiently smooth solution u to the initial value problem associated with the equation ∂tu + iα∂x2u + β∂x3u + iγ u 2u + δ u 2∂xu + εu2∂xū = 0, x, t ε ℝ, is supported in a half line at two different i nstants of time then u ≡ 0. To prove this result we derive a new Carleman type estimate by extending the method introduced by Kenig et al. in [Ann. Inst. H. Poincaré Anal. Non Linéaire 19 (2002) 191-208]. © 2004 Elsevier Inc. All rights reserved. 303 1 188 207 Bourgain, J., Refinements of Strichartz' inequality and applications to 2D-NLS with critical nonlinearity (1998) Internat. Math. Res. Notices, 5, pp. 253-283 Bourgain, J., On the Compactness of the support of solutions of dispersive equations (1997) Internat. Math. Res. Notices, 9, pp. 437-447 Carvajal, X., (2002), Ph.D. Thesis, IMPACarvajal, X., Linares, F., Some properties for a higher order nonlinear Schrödinger equation (2003), PreprintCarvajal, X., Linares, F., A higher order nonlinear Schrödinger equation with variable coefficients (2003) Differential Integral Equations, 16, pp. 1111-1130 Fonseca, G., Linares, F., Ponce, G., Global well-posedness for the modified Korteweg-de Vries equation (1999) Comm. Partial Differential Equations, 24, pp. 683-705 Hasegawa, A., Kodama, Y., Nonlinear pulse propagation in a monomode dielectric guide (1987) IEEE J. Quantum Electronics, 23, pp. 510-524 Kenig, C.E., Ponce, G., Vega, L., On unique continuation for nonlinear Schrödinger equation (2003) Comm. Pure Appl. Math., 56, pp. 1247-1262 Kenig, C.E., Ponce, G., Vega, L., On the support of solutions to the generalized KdV equation (2002) Ann. Inst. H. Poincaré Anal. Non Linéaire, 19, pp. 191-208 Kenig, C.E., Ponce, G., Vega, L., Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle (1993) Comm. Pure Appl. Math., 46, pp. 527-620 Kodama, Y., Optical solitons in a monomode fiber (1985) J. Statist. Phys., 39, pp. 597-614 Laurey, C., The Cauchy problem for a third order nonlinear Schrödinger equation (1997) Nonlinear Anal., 29, pp. 121-158 Lorentz, G., (1996) Approximation of Functions, , New York: Holt, Rinehart and Winston Saut, J.C., Scheurer, B., Unique continuation for some evolution equations (1987) J. Differential Equations, 66, pp. 118-139 Staffilani, G., On the generalized Korteweg-de Vries-type equations (1997) Differential Integral Equations, 10, pp. 777-796 Zhang, B., Unique continuation for the Korteweg-de Vries equation (1992) SIAM J. Math. Anal., 23, pp. 55-71