This paper treats a system of nonlinear Schrödinger equations with delta-functions as initial data. By imposing delta-fUnctions on the initial data, the partial differential equations are reduced into a couple of ODEs, and the behaviors of the solutions are observed in detail. Doi-Shimizu [2] considered a similar problem in case that the powers of nonlinearities coincides in both equations. But this paper removes the coincidence of the powers of nonlinearities, classifies the decay estimates of the global solutions in cases of dissipative nonlinearities, and proves the existence of blowing-up solution in cases that both nonlinearities are amplification
AbstractWe introduce a splitting method for the semilinear Schrödinger equation and prove its conver...
We consider the $L^2$-supercritical nonlinear Schr\"{o}dinger equation with a repulsive Dirac delta ...
In this article we will study the initial value problem for some Schrödinger equations with Dirac-l...
"Harmonic Analysis and Nonlinear Partial Differential Equations". June 30~July 2, 2014. edited by Hi...
In this paper, we study the interaction between a nonlinear focusing Robin type boundary source, a n...
AbstractWe consider a nonlinear semi-classical Schrödinger equation for which it is known that quadr...
This paper is concerned with the initial value problem (IVP) associated to the coupled system of sup...
International audienceWe consider linear and nonlinear Schrödinger equations on a domain Ω with non ...
AbstractIn this paper we study conditions that ensure the existence and uniqueness of the solution t...
"Harmonic Analysis and Nonlinear Partial Differential Equations". July 3~5, 2017. edited by Hideo Ta...
"Harmonic Analysis and Nonlinear Partial Differential Equations". July 3~5, 2017. edited by Hideo Ta...
AbstractWe study the asymptotic behavior in time of solutions to the initial value problem of the no...
For the double power one dimensional nonlinear Schrödinger equation, we establish a complete classif...
Our main research is to study nonlinear Schrodinger equations, especially derivative nonlinear Schrö...
We consider the one-dimensional nonlinear Schr\"odinger equation with focusing, power nonlinearity, ...
AbstractWe introduce a splitting method for the semilinear Schrödinger equation and prove its conver...
We consider the $L^2$-supercritical nonlinear Schr\"{o}dinger equation with a repulsive Dirac delta ...
In this article we will study the initial value problem for some Schrödinger equations with Dirac-l...
"Harmonic Analysis and Nonlinear Partial Differential Equations". June 30~July 2, 2014. edited by Hi...
In this paper, we study the interaction between a nonlinear focusing Robin type boundary source, a n...
AbstractWe consider a nonlinear semi-classical Schrödinger equation for which it is known that quadr...
This paper is concerned with the initial value problem (IVP) associated to the coupled system of sup...
International audienceWe consider linear and nonlinear Schrödinger equations on a domain Ω with non ...
AbstractIn this paper we study conditions that ensure the existence and uniqueness of the solution t...
"Harmonic Analysis and Nonlinear Partial Differential Equations". July 3~5, 2017. edited by Hideo Ta...
"Harmonic Analysis and Nonlinear Partial Differential Equations". July 3~5, 2017. edited by Hideo Ta...
AbstractWe study the asymptotic behavior in time of solutions to the initial value problem of the no...
For the double power one dimensional nonlinear Schrödinger equation, we establish a complete classif...
Our main research is to study nonlinear Schrodinger equations, especially derivative nonlinear Schrö...
We consider the one-dimensional nonlinear Schr\"odinger equation with focusing, power nonlinearity, ...
AbstractWe introduce a splitting method for the semilinear Schrödinger equation and prove its conver...
We consider the $L^2$-supercritical nonlinear Schr\"{o}dinger equation with a repulsive Dirac delta ...
In this article we will study the initial value problem for some Schrödinger equations with Dirac-l...