arXiv subjects

Kaito Kokubu

Publications and source records attributed to Kaito Kokubu.

3 recordsLinked to original sources

arXiv2025

Classification of unstable travelling wave solutions to KdV type equations

We study travelling wave solutions to Korteweg--de Vries type equations which have double power nonlinearities with integer indices, such as the Gardner equation, and fractional dispersion. Whether these equations have ground state solutions depends on signatures of nonlinearities and parity combinations of the two indices. The aim of this study is to give the classification of phenomena of travelling wave solutions from the perspective of the signatures and parities of the indices. In this paper, we focus on unstable travelling wave solutions.

math.AP↗

arXiv2025

Stability of travelling waves to Korteweg--de Vries type equations with fractional dispersion

We study stability of travelling wave solutions to Korteweg--de Vries type equations which has the fractional dispersion and integer-indices double power nonlinearities. It may depend on parity combinations of the two indices and the strength of dispersion whether these equations have a ground state solution. Therefore, we observe the stability phenomena on travelling wave solutions from the perspective of the parities and the dispersion, and we give the classification of phenomena on travelling wave solutions. In this paper, we focus on stable travelling wave solutions.

math.AP↗

arXiv2023

On solitary wave solutions to dispersive equations with double power nonlinearities

We study semilinear elliptic equations with the fractional Laplacian in $\mathbb{R}$. The equations with single power nonlinearities have been observed by Weinstein(1987), Frank--Lenzmann(2013) and so on. We focus on the equations with double power nonlinearities and consider the existence of ground states.

math.AP↗