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Development of computational algorithms for nonlinear wave analysis based on discrete methods for integrable systems

Research Project

Project/Area Number 18K03435
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12040:Applied mathematics and statistics-related
Research InstitutionWaseda University

Principal Investigator

MARUNO KENICHI  早稲田大学, 理工学術院, 教授 (80380674)

Co-Investigator(Kenkyū-buntansha) 太田 泰広  神戸大学, 理学研究科, 教授 (10213745)
筧 三郎  立教大学, 理学部, 教授 (60318798)
Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywords応用可積分系 / 可積分アルゴリズム / 2次元波動パターン / 解構造保存離散化 / 自己適合移動格子スキーム / 離散可積分系 / ソリトン / パフィアン / 構造保存型差分スキーム / 非線形波動 / 2次元非線形波動パターン / 可積分系 / ローグ波 / 三角形分割 / 離散微分幾何 / 離散数理構造
Outline of Final Research Achievements

The goal of our research is to develop innovative computational methods for elucidating complex wave phenomena by using discrete mathematical structures discovered in the study of integrable systems. Specifically, we worked on (1) the development of fast and accurate structure-preserving finite difference schemes based on the methods found in the study of discrete integrable systems, and (2) the development of computational algorithms to predict the time evolution of wave patterns from the information at a certain time.

Academic Significance and Societal Importance of the Research Achievements

本研究課題は可積分系の研究において見出された離散数理構造を積極的に用いて複雑な波動現象解明のための革新的な計算手法を開発することが目標であるが,得られた研究成果によって従来の手法では困難であった計算、解析を可能となった。本研究課題で得られた成果をさらに発展させることで複雑な波動現象の解析が容易になることが期待される。

Report

(6 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (59 results)

All 2023 2022 2021 2020 2019 2018 Other

All Int'l Joint Research (6 results) Journal Article (15 results) (of which Int'l Joint Research: 7 results,  Peer Reviewed: 10 results,  Open Access: 6 results) Presentation (37 results) (of which Int'l Joint Research: 12 results,  Invited: 11 results) Funded Workshop (1 results)

  • [Int'l Joint Research] State University of New York, Buffalo/University of Texas Rio Grande Valley(米国)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] Lishui University(中国)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] オハイオ州立大学/テキサス大学リオグランデバレー校(米国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Lishui大学(中国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Lishui University/East China Normal University(中国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] University of Texas Rio Grande Valley/Ohio State University(米国)

    • Related Report
      2018 Research-status Report
  • [Journal Article] The coupled modified Yajima-Oikawa system: Model derivation and soliton solutions2023

    • Author(s)
      Chen Junchao、Feng Bao-Feng、Maruno Ken-ichi
    • Journal Title

      Physica D: Nonlinear Phenomena

      Volume: 448 Pages: 133695-133695

    • DOI

      10.1016/j.physd.2023.133695

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Soliton resonance and web structure in the Davey-Stewartson system2022

    • Author(s)
      Biondini Gino、Kireyev Dmitri、Maruno Ken-ichi
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 55 Issue: 30 Pages: 305701-305701

    • DOI

      10.1088/1751-8121/ac78db

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A systematic construction of integrable delay-difference and delay-differential analogues of soliton equations2022

    • Author(s)
      Nakata Kenta、Maruno Ken-ichi
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 55 Issue: 33 Pages: 335201-335201

    • DOI

      10.1088/1751-8121/ac7f07

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 一般的な境界条件での自己適合移動格子スキーム2021

    • Author(s)
      丸野健一,太田泰広
    • Journal Title

      津田塾大学数学・計算機科学研究所所報 オンライン研究集会「非線形波動から可積分系へ」

      Volume: 42 Pages: 93-102

    • Related Report
      2020 Research-status Report
  • [Journal Article] Pfaffian 解を持つ Hungry Lotka-Volterra 型方程式2021

    • Author(s)
      志波直明 , 田中悠太 , 丸野健一
    • Journal Title

      津田塾大学数学・計算機科学研究所所報 オンライン研究集会「非線形波動から可積分系へ」

      Volume: 42 Pages: 83-92

    • Related Report
      2020 Research-status Report
  • [Journal Article] BKP方程式のソリトン解の分類2020

    • Author(s)
      田中悠太,丸野健一,児玉裕治
    • Journal Title

      応用力学研究所研究集会報告

      Volume: 2019AO-S2 Pages: 31-36

    • Related Report
      2019 Research-status Report
    • Open Access / Int'l Joint Research
  • [Journal Article] ソリトン方程式のnonlocal reductionとdelay reduction2020

    • Author(s)
      常松愛加,田中悠太,丸野健一
    • Journal Title

      応用力学研究所研究集会報告

      Volume: 2019AO-S2 Pages: 144-150

    • Related Report
      2019 Research-status Report
    • Open Access
  • [Journal Article] Isoperimetric deformations of curves on the Minkowski plane2019

    • Author(s)
      Hyeongki Park, Jun-ichi Inoguchi, Kenji Kajiwara, Ken-ichi Maruno, Nozomu Matsuura and Yasuhiro Ohta
    • Journal Title

      International Journal of Geometric Methods in Modern Physics

      Volume: 印刷中 Issue: 07 Pages: 1950100-1950100

    • DOI

      10.1142/s0219887819501007

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] High-order rogue waves of a long-wave?short-wave model of Newell type2019

    • Author(s)
      Chen Junchao、Chen Liangyuan、Feng Bao-Feng、Maruno Ken-ichi
    • Journal Title

      Physical Review E

      Volume: 100 Issue: 5 Pages: 052216-052216

    • DOI

      10.1103/physreve.100.052216

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] General High-order Rogue Waves of the (1+1)-Dimensional Yajima-Oikawa System2018

    • Author(s)
      Junchao Chen, Yong Chen, Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta
    • Journal Title

      Journal of the Physical Society of Japan

      Volume: 87 Issue: 9 Pages: 094007-094007

    • DOI

      10.7566/jpsj.87.094007

    • NAID

      40021662378

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The Derivative Yajima-Oikawa System: Bright, Dark Soliton and Breather Solutions2018

    • Author(s)
      Junchao Chen, Bao‐Feng Feng, Ken‐ichi Maruno, Yasuhiro Ohta
    • Journal Title

      Studies in Applied Mathematics

      Volume: 141 Issue: 2 Pages: 145-185

    • DOI

      10.1111/sapm.12216

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] DKP方程式のソリトン解のロンスキ型パフィアン表示とネットワーク2018

    • Author(s)
      城戸真弥,渡邉靖之,田中悠太,筧三郎,丸野健一
    • Journal Title

      九州大学応用力学研究所研究集会報告

      Volume: 29AO-S7 (1) Pages: 42-48

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] ソリトンとネットワーク2018

    • Author(s)
      田中悠太,城戸真弥,渡邉靖之,筧三郎,丸野健一
    • Journal Title

      応用力学研究所研究集会報告

      Volume: 29AO-S7 (1) Pages: 131-137

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Davey-Stewartson II 方程式のdark型線ソリトン相互作用と三角形分割2018

    • Author(s)
      巣山大地, 永原新, 丸野健一
    • Journal Title

      九州大学応用力学研究所研究集会報告

      Volume: 29AO-S7 (1) Pages: 138-144

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Davey-Stewartson 2方程式のダーク型線ソリトン相互作用の理論解析2018

    • Author(s)
      巣山大地, 永原新, 丸野健一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2076 Pages: 211-223

    • Related Report
      2018 Research-status Report
    • Open Access
  • [Presentation] Exact solutions and soliton interactions of two-dimensional soliton equations2023

    • Author(s)
      丸野健一
    • Organizer
      研究集会Recent Advances in Nonlinear Water Waves
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 2+1 次元表面張力波における長波短波相互作用とその多成分化2023

    • Author(s)
      沢田陽宏, 筧三郎, 丸野健一
    • Organizer
      日本応用数理学会第19回研究部会連合発表会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Physics-informed neural networkによるソリトン方程式のシミュレーション2023

    • Author(s)
      高橋健,丸野健一
    • Organizer
      日本応用数理学会第19回研究部会連合発表会
    • Related Report
      2022 Annual Research Report
  • [Presentation] 遅延箱玉系のソリトン相互作用パターンの分類と解析2023

    • Author(s)
      松岡宏,中田 健太, 根岸幹太, 丸野 健一
    • Organizer
      日本応用数理学会第19回研究部会連合発表会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Integrable discretizations of integrable nonlinear differential equa- tions with hodograph transformations2022

    • Author(s)
      丸野健一
    • Organizer
      Isaac Newton Institute for Mathematical Sciences セミナー
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 遅延ソリトン方程式の構成と遅延箱玉系2022

    • Author(s)
      中田 健太, 根岸幹太, 丸野 健一
    • Organizer
      研究集会「非線形波動から可積分系へ2022」
    • Related Report
      2022 Annual Research Report
  • [Presentation] 2+1 次元表面張力波における長波短波相互作用2022

    • Author(s)
      沢田陽宏, 筧三郎, 丸野健一
    • Organizer
      研究集会「非線形波動から可積分系へ2022」
    • Related Report
      2022 Annual Research Report
  • [Presentation] N-ソリトン解を持つ遅延 KdV、遅延ブシネスク、遅延 KP 方程式の構成2022

    • Author(s)
      中田 健太, 丸野 健一
    • Organizer
      日本応用数理学会2022年度年会
    • Related Report
      2022 Annual Research Report
  • [Presentation] 遅延離散ロトカ・ボルテラ方程式の超離散化と遅延箱玉系2022

    • Author(s)
      根岸幹太, 中田 健太, 丸野 健一
    • Organizer
      日本応用数理学会2022年度年会
    • Related Report
      2022 Annual Research Report
  • [Presentation] ホドグラフ変換に関わる非線形微分方程式の解構造を保存する離散化: 解構造を保存する適合格子細分化法2022

    • Author(s)
      丸野健一
    • Organizer
      京都大学数理解析研究所研究集会「可積分系数理の発展とその応用」
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] ホドグラフ変換が関わる非線形微分方程式の解構造を保存する離散化:解構造を保存する適合格子細分化法2022

    • Author(s)
      丸野 健一
    • Organizer
      モビリティ数理オンラインセミナー
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] 可積分系と非線形水波に関連する最近の研究について2022

    • Author(s)
      丸野 健一
    • Organizer
      オンライン研究集会「大振幅・非線形海洋波の数理の展望」
    • Related Report
      2021 Research-status Report
  • [Presentation] Pfaffian解を持つHungry Lotka-Volterra型方程式とソリトン解2021

    • Author(s)
      志波 直明 , 田中 悠太 , 中田 健太 , 丸野 健一
    • Organizer
      日本応用数理学会2021年度年会
    • Related Report
      2021 Research-status Report
  • [Presentation] N ソリトン解を持つ遅延ソリトン方程式の構成法2021

    • Author(s)
      中田 健太, 丸野 健一
    • Organizer
      オンライン研究集会「非線形波動と可積分系」
    • Related Report
      2021 Research-status Report
  • [Presentation] パフィアン解を持つ Hungry Lotka-Volterra 型方程式のソリトン相互作用2021

    • Author(s)
      志波 直明, 田中 悠太, 中田 健太, 丸野 健一
    • Organizer
      オンライン研究集会「非線形波動と可積分系」 2021年11月6日
    • Related Report
      2021 Research-status Report
  • [Presentation] 一般的な境界条件での自己適合移動格子スキーム2021

    • Author(s)
      丸野 健一
    • Organizer
      第5回 精度保証付き数値計算の実問題への応用研究集会 (NVR 2021)
    • Related Report
      2021 Research-status Report
  • [Presentation] SIR モデルの解構造を保存する離散化と厳密解2021

    • Author(s)
      丸野健一,田中悠太
    • Organizer
      日本応用数理学会第17回研究部会連合発表会
    • Related Report
      2020 Research-status Report
  • [Presentation] 多ソリトン解を持つ可積分系の遅延化2021

    • Author(s)
      中田健太, 丸野健一
    • Organizer
      日本応用数理学会第17回研究部会連合発表会
    • Related Report
      2020 Research-status Report
  • [Presentation] 一般的な境界条件での自己適合移動格子スキームと数値計算2021

    • Author(s)
      丸野健一,太田泰広
    • Organizer
      日本物理学会第76回年次大会
    • Related Report
      2020 Research-status Report
  • [Presentation] 自己適合移動格子スキームの最近の進展2021

    • Author(s)
      丸野健一
    • Organizer
      研究集会「非線形海洋波の数理とその応用」
    • Related Report
      2020 Research-status Report
  • [Presentation] 一般的な境界条件での自己適合移動格子スキーム2020

    • Author(s)
      丸野健一,太田泰広
    • Organizer
      オンライン研究集会「非線形波動から可積分系へ」津田塾大学数学計算機科学研究所
    • Related Report
      2020 Research-status Report
  • [Presentation] Pfaffian 解を持つ Hungry Lotka-Volterra 型方程式2020

    • Author(s)
      志波直明 , 田中悠太 , 丸野健一
    • Organizer
      オンライン研究集会「非線形波動から可積分系へ」津田塾大学数学計算機科学研究所
    • Related Report
      2020 Research-status Report
  • [Presentation] The 2nd JNMP Conference on Nonlinear Mathematical Physics2019

    • Author(s)
      Ken-ichi Maruno
    • Organizer
      Integrable discretizations of integrable systems and motion of discrete curves
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Integrable discretizations of the complex WKI equation and numerical computation of a vortex filament2019

    • Author(s)
      Ken-ichi Maruno
    • Organizer
      ISLAND V: Integrable systems, special functions and combinatorics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Integrable discretizations of the complex WKI equation and numerical computation of a vortex filament2019

    • Author(s)
      Ken-ichi Maruno
    • Organizer
      International Congress on Industrial and Applied Mathematics (ICIAM) 2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 自己適合移動格子スキームの境界条件2019

    • Author(s)
      丸野健一
    • Organizer
      研究集会「非線形波動研究の多様性」
    • Related Report
      2019 Research-status Report
  • [Presentation] BKP方程式のソリトン解の分類2019

    • Author(s)
      田中悠太,丸野健一,児玉裕治
    • Organizer
      研究集会「非線形波動研究の多様性」
    • Related Report
      2019 Research-status Report
  • [Presentation] ソリトン方程式のnonlocal reductionとdelay reduction2019

    • Author(s)
      常松愛加,田中悠太,丸野健一
    • Organizer
      研究集会「非線形波動研究の多様性」
    • Related Report
      2019 Research-status Report
  • [Presentation] Numerical and analytical studies of the KP1 equation2019

    • Author(s)
      Ken-ichi Maruno
    • Organizer
      Mini Symposium on Integrable Systems
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Integrable discretization of soliton equations and numerical computations2019

    • Author(s)
      Ken-ichi Maruno
    • Organizer
      2019 28th Annual Workshop on Differential Equations
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] An integrable discretization of the complex WKI equation and a vortex filament2019

    • Author(s)
      Ken-ichi Maruno, Shinya Kido, Satomi Nakamura
    • Organizer
      AMS Spring Central and Western Joint Sectional Meeting
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] BKP方程式のGram型Pfaffian解とそのソリトン相互作用2019

    • Author(s)
      田中悠太,丸野健一,児玉裕治
    • Organizer
      日本応用数理学会2019年研究部会連合発表会
    • Related Report
      2018 Research-status Report
  • [Presentation] Discrete structures of integrable systems and its applications2018

    • Author(s)
      Ken-ichi Maruno
    • Organizer
      2018 ICIAM Workshop
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] DKP solitons and networks2018

    • Author(s)
      Ken-ichi Maruno
    • Organizer
      The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] The interactions of dark line solitons in the Davey-Stewartson II system2018

    • Author(s)
      Ken-ichi Maruno
    • Organizer
      Workshop on Nonlinear Water Waves
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] KP方程式と結合型KP方程式のソリトン相互作用の解析2018

    • Author(s)
      田中悠太, 城戸真弥, 渡邉靖之, 丸野健一, 筧三郎
    • Organizer
      非線形波動現象の数理とその応用
    • Related Report
      2018 Research-status Report
  • [Presentation] Soliton interactions of the KP and DKP equations and their network diagrams2018

    • Author(s)
      Ken-ichi Maruno
    • Organizer
      JSPS Almuni Association Seminar
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Funded Workshop] Symmetries and Integrability of Difference Equations 132018

    • Related Report
      2018 Research-status Report

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Published: 2018-04-23   Modified: 2024-01-30  

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