Remark on the stabilization for a Schrödinger equation with double power nonlinearity. (English) Zbl 1428.35530
Summary: In this paper we study the decay rates of the solutions for a Schrödinger equation with double power nonlinearity in \(L^p(\mathbb{R})\)-norm for \(2 < p \leq \infty\). We give some numerical examples to illustrate our analytical results.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35B35 | Stability in context of PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
References:
| [1] | Kartavenko, V. G., Soliton-like solutions in nuclear hydrodynamics, Sov. J. Nucl. Phys., 40, 240-246 (1984) · Zbl 0596.76022 |
| [2] | Kumar, A.; Sarkar, S. N.; Ghatak, A. K., Effect of fifth-order non-linearity in refractive index on Gaussian pulse propagation in lossy optical fiber, Opt. Lett., 11, 321-323 (1986) |
| [3] | Ginibre, J.; Velo, G., On a class of Schrödinger equations III, Ann. Inst. Henri Poincare Phys. Theor., 28, 287-316 (1978) · Zbl 0397.35012 |
| [4] | Hayashi, N.; Nakamitsu, K.; Tsutsumi, M., On solutions on the initial value problem for the nonlinear Schrödinger equations in One Space Dimension, Math. Z., 192, 637-650 (1986) · Zbl 0617.35025 |
| [5] | Cazenave, T., (Semilinear SchrÖdinger Equations. Semilinear SchrÖdinger Equations, Lect. Notes in Math., vol. 10 (2003), New York University. Courant Institute of Mathematicas Sciences, Amer. Math. Soc. RI: New York University. Courant Institute of Mathematicas Sciences, Amer. Math. Soc. RI New York) · Zbl 1055.35003 |
| [6] | Friedman, A., Partial Differential Equations (1969), Holt-Rinehart and Winston: Holt-Rinehart and Winston New York · Zbl 0224.35002 |
| [7] | Halanay, A., Differential Equations, Stability, Oscillations, Time, Lags (1966), Academic Press: Academic Press New York, London · Zbl 0144.08701 |
| [8] | Delfour, M.; Fortin, M.; Payre, G., Finite-difference solutions of a nonlinear Schrödinger equation, J. Comput. Phys., 44, 227-288 (1981) · Zbl 0477.65086 |
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