Abstract
Conservation laws of the charge and of the energy are proved for nonlinear Schrödinger equations with nonlinearities of gauge invariance in a way independent of approximate solutions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cazenave, T.: Semilinear Schrödinger Equations. Courant Lecture Notes in Mathematics, Vol. 10. American Mathematical Society (2003)
Ginibre, J.: An introduction to nonlinear Schrödinger equations. In: Agemi, R., Giga, Y., Ozawa, T. (eds.), Nonlinear Waves. GAKUTO International Series, Mathematical Sciences and Applications, vol. 10. Gakk\(\bar{o}\)tosho, Tokyo (1997)
Ginibre, J., Velo, G.: On a class of nonlinear Schrödinger equations, I. The Cauchy problem. J. Funct. Anal. 32, 1–32 (1979)
Kato, T.: On nonlinear Schrödinger equations. Ann. Inst. H. Poincaré, Phys. Théor. 46, 113–129 (1987)
Kato, T.: Nonlinear Schrödinger equations. In: Holden, H., Jensen, A. (eds.), Schrödinger Operators. Lecture Notes in Phys. 345, Springer (1989)
Sulem, C., Sulem, P.L.: The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse. Applied Mathematical Sciences, Vol. 139. Springer (1999)
Tsutsumi, Y.: L2-solutions for nonlinear Schrödinger equations and nonlinear groups. Funkcialaj Ekvacioj 30, 115–125 (1987)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ozawa, T. Remarks on proofs of conservation laws for nonlinear Schrödinger equations. Calc. Var. 25, 403–408 (2006). https://doi.org/10.1007/s00526-005-0349-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00526-005-0349-2