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Nowhere continuity of the flow map of an integrable derivative nonlinear Schrödinger system on the torus
Toshiki Kondo
We consider a derivative nonlinear Schrödinger system called the Chen-Lee-Liu type system on the torus. This system is known as a completely integrable system. We prove the flow ma…
Norm inflation for quadratic derivative fractional nonlinear Schrödinger equations
Toshiki Kondo, Mamoru Okamoto
We consider the Cauchy problem for quadratic derivative fractional nonlinear Schrödinger equations on or . We determine the sharp exponents of the fraction…
Well- and Ill-posedness of the Cauchy problem for derivative fractional nonlinear Schrödinger equations on the torus
Takamori Kato, Toshiki Kondo, Mamoru Okamoto
We consider the Cauchy problem for derivative fractional Schrödinger equations (fNLS) on the torus . Recently, the second and third authors established a necessary and s…
Well- and ill-posedness of the Cauchy problem for semi-linear Schrödinger equations on the torus
Toshiki Kondo, Mamoru Okamoto
We consider the Cauchy problem for semi-linear Schrödinger equations on the torus . We establish a necessary and sufficient condition on the polynomial nonlinearity for…
Norm inflation for a higher-order nonlinear Schrödinger equation with a derivative on the circle
Toshiki Kondo, Mamoru Okamoto
We consider a periodic higher-order nonlinear Schrödinger equation with the nonlinearity , where is a natural number. We prove the norm inflation in a subspac…