32 citations · 178 across the 24 of their papers we have counts for
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Well-posedness for KdV-type equations with quadratic nonlinearity
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
We consider the Cauchy problem of the KdV-type equation \[ \partial_t u + \frac{1}{3} \partial_x^3 u = c_1 u \partial_x^2u + c_2 (\partial_x u)^2, \quad u(0)=u_0. \] Pilod (2008) s…
Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations with radial initial data
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
In the present paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schrödinger equations. This system was introduced by M. Colin and T. Colin (200…
Sharp ill-posedness of the Dirac-Klein-Gordon system in one dimension
Shuji Machihara, Mamoru Okamoto
We show the ill-posedness of the Cauchy problem for the Dirac-Klein-Gordon system in one dimension in the critical Sobolev space. From this, we finish the classification of the reg…
Asymptotic behavior of solutions to a higher-order KdV-type equation with critical nonlinearity
Mamoru Okamoto
We consider the Cauchy problem of the higher-order KdV-type equation: \[ \partial_t u + \frac{1}{\mathfrak{m}} |\partial_x|^{\mathfrak{m}-1} \partial_x u = \partial_x (u^{\mathfrak…