Toshiki Kondo

activity

20242026

collaborators

5 papers

math.AP2026

Nowhere continuity of the flow map of an integrable derivative nonlinear SchrÃ¶dinger system on the torus

Toshiki Kondo

We consider a derivative nonlinear SchrÃ¶dinger system called the Chen-Lee-Liu type system on the torus. This system is known as a completely integrable system. We prove the flow m…

math.AP2026

Norm inflation for quadratic derivative fractional nonlinear SchrÃ¶dinger equations

Toshiki Kondo, Mamoru Okamoto

We consider the Cauchy problem for quadratic derivative fractional nonlinear SchrÃ¶dinger equations on $R$ or $T$ . We determine the sharp exponents of the fractio…

math.AP2025

Well- and Ill-posedness of the Cauchy problem for derivative fractional nonlinear SchrÃ¶dinger equations on the torus

Takamori Kato, Toshiki Kondo, Mamoru Okamoto

We consider the Cauchy problem for derivative fractional SchrÃ¶dinger equations (fNLS) on the torus $T$ . Recently, the second and third authors established a necessary and…

math.AP2025

Well- and ill-posedness of the Cauchy problem for semi-linear SchrÃ¶dinger equations on the torus

Toshiki Kondo, Mamoru Okamoto

We consider the Cauchy problem for semi-linear SchrÃ¶dinger equations on the torus $T$ . We establish a necessary and sufficient condition on the polynomial nonlinearity for…

math.AP2024

Norm inflation for a higher-order nonlinear SchrÃ¶dinger equation with a derivative on the circle

Toshiki Kondo, Mamoru Okamoto

We consider a periodic higher-order nonlinear SchrÃ¶dinger equation with the nonlinearity $u^{k} \partial_{x} u$ , where $k$ is a natural number. We prove the norm inflation in a subspa…