WSA62000 Geometric and Algebraic Analysis B

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program

Lecture Code WSA62000 Subject Classification Specialized Education

Subject Name 総合数理基礎講義Ｂ

Subject Name
（Katakana）ソウゴウスウリキソコウギビー

Subject Name in
English Geometric and Algebraic Analysis B

Instructor MIZUMACHI TETSU,SHIBUYA KAZUHIRO,HASHIMOTO SHINTARO

Instructor
(Katakana) ミズマチ　テツ,シブヤ　カズヒロ,ハシモト　シンタロウ

Campus Higashi-Hiroshima Semester/Term 1st-Year,  Second Semester,  3Term

Days, Periods, and Classrooms (3T) Mon5-8：IAS C807

Lesson Style Lecture Lesson Style
(More Details) Face-to-face

Writing on blackboard.

Credits 2.0 Class Hours/Week 4 Language of Instruction B : Japanese／English

Course Level 5 : Graduate Basic

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students M1, M2

Keywords

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students)

Class Objectives
/Class Outline I will llustrate some elementary results on the KdV equation.  Topics might be changed.

Class Schedule lesson1 Euler Equations
lesson2 Derivation of long wave models (1)
lesson3 Derivation of long wave models (2)
lesson4 KdV and KP equations
lesson5 Traveling wave solutions of the KdV equation
lesson6 KdV solitons (1)
lesson7 KdV solitons (2)
lesson8 Noether's theorem
lesson9 A Lax pair and conservation laws of KdV (1)
lesson10 A Lax pair and conservation laws of KdV (2)
lesson11 D-operators and bilinear forms (1)
lesson12 D-operators and bilinear forms (2)
lesson13 Line solitons of the KP-II equation (1)
lesson14 Line solitons of the KP-II equation (2)
lesson15 Summary

Text/Reference
Books,etc. 1) Morikazu, Toda, Nonlinear Waves and Solitons
(Mathematics and its Applications (Japanese Series) vol 5) (Tokyo:Kluwer)
2) R. Hirota, The Direct Method in Soliton Theory (Cambridge University Press)
3)P. D. Lax, Integrals of nonlinear equations of evolution and solitary waves. Comm. Pure Appl. Math. 21 (1968), 467–490.

PC or AV used in
Class,etc. Microsoft Teams

(More Details) Blackboard

Learning techniques to be incorporated

Suggestions on
Preparation and
Review Consult the literature introduced during the lectures.

Requirements

Grading Method There shall be reporting assignments in the end of classes.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

Other

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2026Year	School/Graduate School	Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program
Lecture Code	WSA62000	Subject Classification	Specialized Education
Subject Name	総合数理基礎講義Ｂ
Subject Name （Katakana）	ソウゴウスウリキソコウギビー
Subject Name in English	Geometric and Algebraic Analysis B
Instructor	MIZUMACHI TETSU,SHIBUYA KAZUHIRO,HASHIMOTO SHINTARO
Instructor (Katakana)	ミズマチ　テツ,シブヤ　カズヒロ,ハシモト　シンタロウ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, Second Semester, 3Term
Days, Periods, and Classrooms	(3T) Mon5-8：IAS C807
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face
Writing on blackboard.
Credits	2.0	Class Hours/Week	4	Language of Instruction	B : Japanese／English
Course Level	5 : Graduate Basic
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students	M1, M2
Keywords
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)
Class Objectives /Class Outline	I will llustrate some elementary results on the KdV equation. Topics might be changed.
Class Schedule	lesson1 Euler Equations lesson2 Derivation of long wave models (1) lesson3 Derivation of long wave models (2) lesson4 KdV and KP equations lesson5 Traveling wave solutions of the KdV equation lesson6 KdV solitons (1) lesson7 KdV solitons (2) lesson8 Noether's theorem lesson9 A Lax pair and conservation laws of KdV (1) lesson10 A Lax pair and conservation laws of KdV (2) lesson11 D-operators and bilinear forms (1) lesson12 D-operators and bilinear forms (2) lesson13 Line solitons of the KP-II equation (1) lesson14 Line solitons of the KP-II equation (2) lesson15 Summary
Text/Reference Books,etc.	1) Morikazu, Toda, Nonlinear Waves and Solitons (Mathematics and its Applications (Japanese Series) vol 5) (Tokyo:Kluwer) 2) R. Hirota, The Direct Method in Soliton Theory (Cambridge University Press) 3)P. D. Lax, Integrals of nonlinear equations of evolution and solitary waves. Comm. Pure Appl. Math. 21 (1968), 467–490.
PC or AV used in Class,etc.	Microsoft Teams
(More Details)	Blackboard
Learning techniques to be incorporated
Suggestions on Preparation and Review	Consult the literature introduced during the lectures.
Requirements
Grading Method	There shall be reporting assignments in the end of classes.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
Other
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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