### Abstract

In this article, we prove the existence of a non-scattering solution, which is minimal in some sense, to the mass-subcritical generalized Korteweg–de Vries (gKdV) equation in the scale critical Lˆ^{r} space where Lˆ^{r}={f∈S^{′}(R)|‖f‖_{Lˆr }=‖fˆ‖_{Lr′ }<∞}. We construct this solution by a concentration compactness argument. Then, key ingredients are a linear profile decomposition result adopted to Lˆ^{r}-framework and approximation of solutions to the gKdV equation which involves rapid linear oscillation by means of solutions to the nonlinear Schrödinger equation.

Original language | English |
---|---|

Pages (from-to) | 283-326 |

Number of pages | 44 |

Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |

Volume | 35 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 1 2018 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematical Physics

### Cite this

**Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg–de Vries equation.** / Masaki, Satoshi; Segata, Junichi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg–de Vries equation

AU - Masaki, Satoshi

AU - Segata, Junichi

PY - 2018/3/1

Y1 - 2018/3/1

N2 - In this article, we prove the existence of a non-scattering solution, which is minimal in some sense, to the mass-subcritical generalized Korteweg–de Vries (gKdV) equation in the scale critical Lˆr space where Lˆr={f∈S′(R)|‖f‖Lˆr =‖fˆ‖Lr′ <∞}. We construct this solution by a concentration compactness argument. Then, key ingredients are a linear profile decomposition result adopted to Lˆr-framework and approximation of solutions to the gKdV equation which involves rapid linear oscillation by means of solutions to the nonlinear Schrödinger equation.

AB - In this article, we prove the existence of a non-scattering solution, which is minimal in some sense, to the mass-subcritical generalized Korteweg–de Vries (gKdV) equation in the scale critical Lˆr space where Lˆr={f∈S′(R)|‖f‖Lˆr =‖fˆ‖Lr′ <∞}. We construct this solution by a concentration compactness argument. Then, key ingredients are a linear profile decomposition result adopted to Lˆr-framework and approximation of solutions to the gKdV equation which involves rapid linear oscillation by means of solutions to the nonlinear Schrödinger equation.

UR - http://www.scopus.com/inward/record.url?scp=85019096058&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019096058&partnerID=8YFLogxK

U2 - 10.1016/j.anihpc.2017.04.003

DO - 10.1016/j.anihpc.2017.04.003

M3 - Article

VL - 35

SP - 283

EP - 326

JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

SN - 0294-1449

IS - 2

ER -