4 papers · 1 filter
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…
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…
Global solution for the stochastic nonlinear Schrödinger system with quadratic interaction in four dimensions
Masaru Hamano, Shunya Hashimoto, Shuji Machihara
We discuss the global existence of solutions to a system of stochastic Schrödinger equations with multiplicative noise. Our setting of the quadratic nonlinear terms in dimension 4…