Najman, B. The nonrelativistic limit of the nonlinear Dirac equation. (English) Zbl 0746.35036 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 9, No. 1, 3-12 (1992). Summary: It is proved that there exist solutions of the nonlinear Dirac equation, smooth in time, on a time interval which is independent of \(c\). Moreover after multiplication of a phase factor (dependent on \(c\)) these solutions converge to the solution of a coupled system of nonlinear Schrödinger type equations. Cited in 19 Documents MSC: 35Q40 PDEs in connection with quantum mechanics 35Q55 NLS equations (nonlinear Schrödinger equations) 35B25 Singular perturbations in context of PDEs 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics Keywords:solution of a coupled system of nonlinear Schrödinger type equations × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] Balabane, M.; Cazanave, T.; Douady, A.; Merle, F., Existence of Excited States for a Nonlinear Dirac Field, Commun. Math. Phys., Vol. 119, 153-176 (1988) · Zbl 0696.35158 [2] Cazenave, T.; Vazquez, L., Existence of Localized Solutions for a Classical Nonlinear Dirac Field, Commun. Math. Phys., Vol. 105, 35-47 (1986) · Zbl 0596.35117 [3] Cazenave, T., Stationary States of Nonlinear Dirac Equation, (Brezis, H.; Crandall, M. G.; Kappel, F., Semigroups, Theory and Applications, Vol. I (1986), Longman Scientific and Technical: Longman Scientific and Technical Essex), 36-42, Pitman Research Notes in Math. Sciences · Zbl 0611.34003 [5] Najman, B., The Nonrelativistic Limit of the Klein-Gordon and Dirac Equations, In Differential Equations with Applications in Biology, Physics and Engineering, (Goldstein, J.; Kappel, F.; Schappacher, W., Lect. Notes Pure Appi. Math., No. 133 (1991), Marcel Dekker), 291-299 · Zbl 0744.35038 [6] Veselić, K., Perturbation of Pseudoresolvents and Analyticity in \(1/c\) in Relativistic Quantum Mechanics, Commun. Math. Phys., Vol. 22, 27-43 (1971) · Zbl 0212.15701 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.