6 papers
A Unified Integral Equation Approach to Conservation Laws for Nonlinear Schrödinger Equations
Shuji Machihara, Hayato Miyazaki, Tohru Ozawa
We present a unified framework for the rigorous derivation of conservation laws and related identities for nonlinear Schrödinger equations with power-type nonlinearities. This app…
A comparison of the weakest contractive conditions for Banach and Kannan mappings
Shunya Hashimoto, Misako Kikkawa, Shuji Machihara +1
We study the weakest convergence-type conditions for fixed point results for Banach and Kannan mappings. Building on Suzuki's weakest condition for Banach mappings and our previous…
Exponential Decay of -Solutions to Stochastic Nonlinear Schrödinger Equations Driven by Continuous Martingales
Isamu Dôku, Shunya Hashimoto, Shuji Machihara
We investigate the global well-posedness and asymptotic behavior of -solutions to stochastic nonlinear Schrödinger equations with multiplicative noise driven by continuous sq…
On the weakest conditions for the existence of fixed points of Kannan and Chatterjea type contractions
Shunya Hashimoto, Misako Kikkawa, Shuji Machihara +1
In this paper, we study the weakest possible conditions for fixed point theorems involving two classes of mappings defined by Kannan and Chatterjea. Our approach relies on the so-c…
Remarks on the derivation of the virial identity for nonlinear Schrödinger equations
Tomoyuki Ikeda, Shuji Machihara, Hayato Miyazaki +1
We revisit the derivation of the virial identity for nonlinear Schrödinger equations. In \cite{O06, FM17}, several conservation laws, such as for the charge and the energy, were d…
The well-posedness of the stochastic nonlinear Schrödinger equations in
Isamu Dôku, Shunya Hashimoto, Shuji Machihara
The Cauchy problem for the stochastic nonlinear Schrödinger equation with multiplicative noise is considered where the nonlinear term is of power type and the noise coefficients a…