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Abstract:

The initial value problem for the derivative nonlinear Schrödinger equation (DNLS) was studied. The existence of global weak solutions and smoothing effect for DNLS was demonstrated. Compactness was required to obtain the dispersive smoothing properties of the Schrödinger equation.

Registro:

Documento: Artículo
Título:Weak solutions for the derivative nonlinear Schrödinger equation
Autor:Rial, D.F.
Filiación:Dpto De Matematica Fac De CS, Exactas Y Naturales, UBA Pab I, 1428 Capital, Argentina
Palabras clave:Derivative nonlinear Schrödinger equation; Nonlocal dissipation; Smoothing effect; Weak solutions; Convergence of numerical methods; Initial value problems; Mathematical transformations; Theorem proving; Shrodinger equations; Nonlinear equations
Año:2002
Volumen:49
Número:2
Página de inicio:149
Página de fin:158
DOI: http://dx.doi.org/10.1016/S0362-546X(00)00217-0
Título revista:Nonlinear Analysis, Theory, Methods and Applications
Título revista abreviado:Nonlinear Anal Theory Methods Appl
ISSN:0362546X
CODEN:NOAND
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v49_n2_p149_Rial

Referencias:

  • De Bouvard, A., (1990) Analytic solutions to non elliptic nonlinear Schrödinger equation, , Preprint
  • Cazenave, T., An introduction to nonlinear schrödinger equation (1990) Textos de Métodos Matemáticos, 22. , Universidad de Rio de Janeiro
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  • Kato, T., On the Cauchy problem for the (generalized) Korteweg-de Vries equation (1983) Advances in Mathematics Supplementary Studies Studies in Appl. Math., 8, pp. 93-128
  • Kaup, D.J., Newell, A.C., An exact solution for a derivative nonlinear Schrödinger equation (1978) J. Math Phys., 19, pp. 798-801
  • Kenig, C.E., Ponce, G., Vega, L., Well-posedness and scattering results for the Korteweg-de Vries equation (1991) J. Amer. Math. Soc., 4, pp. 323-347
  • Kenig, C.E., Ponce, G., Vega, L., Small solutions to nonlinear Schrödinger equation (1993) Ann. Inst. Henri Poincaré, Anal. nonlinéaire, 10, pp. 255-288
  • Lions, J.L., (1969) Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, , Gauthier-Villars, Paris
  • Mjølhus, E., On the modulational instability of hydromagnetic waves parallel to the magnetic field (1976) J. Plasma Phys., 16, pp. 321-334
  • Ponce, G., On the global well-posedness of the Benjamin-Ono equation (1991) Diff. Int. Eq., 4, pp. 527-542

Citas:

---------- APA ----------
(2002) . Weak solutions for the derivative nonlinear Schrödinger equation. Nonlinear Analysis, Theory, Methods and Applications, 49(2), 149-158.
http://dx.doi.org/10.1016/S0362-546X(00)00217-0
---------- CHICAGO ----------
Rial, D.F. "Weak solutions for the derivative nonlinear Schrödinger equation" . Nonlinear Analysis, Theory, Methods and Applications 49, no. 2 (2002) : 149-158.
http://dx.doi.org/10.1016/S0362-546X(00)00217-0
---------- MLA ----------
Rial, D.F. "Weak solutions for the derivative nonlinear Schrödinger equation" . Nonlinear Analysis, Theory, Methods and Applications, vol. 49, no. 2, 2002, pp. 149-158.
http://dx.doi.org/10.1016/S0362-546X(00)00217-0
---------- VANCOUVER ----------
Rial, D.F. Weak solutions for the derivative nonlinear Schrödinger equation. Nonlinear Anal Theory Methods Appl. 2002;49(2):149-158.
http://dx.doi.org/10.1016/S0362-546X(00)00217-0