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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 appr…
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 de…
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…
Blow-up solutions for non-scale-invariant nonlinear Schrödinger equation in one dimension
Masaru Hamano, Masahiro Ikeda, Shuji Machihara
In this paper, we consider the mass-critical nonlinear Schrödinger equation in one dimension. Ogawa--Tsutsumi [19] proved a blow-up result for negative energy solution by using a s…
Non-delay limit in the energy space from the nonlinear damped wave equation to the nonlinear heat equation
Takahisa Inui, Shuji Machihara
We consider a singular limit problem from the damped wave equation with a power type nonlinearity to the corresponding heat equation. We call our singular limit problem non-delay l…
Blowup solutions for the nonlinear Schrödinger equation with complex coefficient
Shota Kawakami, Shuji Machihara
We construct a finite time blow up solution for the nonlinear Schrödinger equation with the power nonlinearity whose coefficient is complex number. We generalize the range of both…