Dissipative property for higher order nonlinear Schrödinger equation

被引：0
作者：
Naumkin P.I. [1 ]
Sánchez-Suárez I. [2 ]
机构：
[1] Centro de Ciencias Matemáticas UNAM Campus Morelia, AP 61-3 (Xangari) Morelia CP 58089, Michoacán, México
[2] Universidad Politécnica de Uruapan
来源：
Nonlinear Analysis, Theory, Methods and Applications | 2019年 / 188卷
关键词：
Decay estimates; Dispersive equations; Nonlinear Schrödinger equation; Scattering theory;
D O I：
10.1016/j.na.2019.05.018
中图分类号：
O172 [微积分];
学科分类号：
摘要：
We consider the Cauchy problem for the higher-order nonlinear Schrödinger equation i∂tu+1/2∂x 2u−1/4∂x 4u=i3λ1u3+λ2u2u,t>1,x∈R,u1,x=u0x,x∈R,where the coefficients 0<λ1<λ2. The aim of the present paper is to prove the global existence of solutions to (??). Also we find the large time decay estimates for the solutions. © 2019 Elsevier Ltd
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页码：91 / 124
页数：33
相关论文
共 31 条
[1]  
Calderon A.P., Vaillancourt R., A class of bounded pseudo-differential operators, Proc. Natl. Acad. Sci. USA, 69, pp. 1185-1187, (1972)
[2]  
Cazenave T., Semilinear Schrödinger equations, Courant Institute of Mathematical Sciences, (2003)
[3]  
Coifman R.R., Meyer Y., Au Dela Des Operateurs Pseudo-Differentiels, (1978)
[4]  
Cordes H.O., On compactness of commutators of multiplications and convolutions, and boundedness of pseudodifferential operators, J. Funct. Anal., 18, pp. 115-131, (1975)
[5]  
Dysthe K.B., Note on a modification to the nonlinear Schrödinger equation for application to deep water waves, Proc. R. Soc. Lond. Ser. A, 369, pp. 105-114, (1979)
[6]  
Fanelli L., Dispersive equations in quantum mechanics, Rend. Mat. Appl., 28, 7, pp. 3-4, (2008)
[7]  
Fedoryuk M.V., Asymptotic methods in analysis, Analysis. I. Integral Representations and Asymptotic Methods, Encyclopaedia of Mathematical Sciences, 13, (1989)
[8]  
Fukumoto Y., Motion of a curved vortex filament: higher-order asymptotics, Proc. IUTAM Symp. Geom. Stat. Turbul, pp. 211-216, (2001)
[9]  
Guo C., Cui S., Global existence of solutions for a fourth-order nonlinear Schrödinger equation, Appl. Math. Lett., 19, pp. 706-711, (2006)
[10]  
Hao C., Hsian L., Wang B., Wellposedness for the fourth order nonlinear Schrödinger equations, J. Math. Anal. Appl., 320, pp. 246-265, (2006)
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