Collapse Rate of Solutions of the Cauchy Problem for the Nonlinear Schrödinger Equation

被引：0
作者：
Sh. M. Nasibov
机构：
[1] Baku State University,Institute of Applied Mathematics
来源：
Theoretical and Mathematical Physics | 2020年 / 203卷
关键词：
nonlinear Schrödinger evolution equation; Cauchy problem; collapse; collapse rate; interpolation inequality;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove that solutions of the Cauchy problem for the nonlinear Schrödinger equation with certain initial data collapse in a finite time, whose exact value we estimate from above. We obtain an estimate from below for the solution collapse rate in certain norms.
引用
收藏
页码：726 / 733
页数：7
相关论文
共 37 条
[1]  
Zakharov V E(1971)Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media Soviet JETP 34 62-69
[2]  
Shabat A B(1974)Theory of the propagation of high-power laser radiation in a nonlinear medium Sov. Phys. Usp. 16 658-679
[3]  
Lugovoi V N(1986)Blow-up in nonlinear Schrödinger equations: I. A general review Phys. Scr. 33 481-497
[4]  
Prokhorov A M(1985)On stability, collapse, decay, and self-trapping of solutions of a nonlinear Schrödinger equation Sov. Math. Dokl. 32 784-788
[5]  
Rydpal K(1990)Optimal constants in some Sobolev inequalities and their applications to the nonlinear Schrödinger equation Soviet Math. Dokl. 40 110-115
[6]  
Rasmussen J J(1969)On the Cauchy problem for the Ginzburg-Landau equation [in Russian] Dinamika Sploshnoi Sredy 1 180-194
[7]  
Nasibov Sh M(1970)The Cauchy problem for the nonlinear Schrödinger equation [in Russian] Differ. Equ. 6 137-146
[8]  
Nasibov Sh M(2013)Gradient blow-up of solutions to the Cauchy problem for the Schrödinger equation Proc. Steklov Inst. Math. 283 165-180
[9]  
Shabat A B(2018)A reliable algorithm for solving linear and nonlinear Schrödinger equations Appl. Comput. Math. 17 151-160
[10]  
Zhiber A V(1989)On a nonlinear Schrödinger equation with a dissipative term Soviet Math. Dokl. 39 59-63
1234