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MATH 337 - INTRODUCTION TO SOLITON THEORY
Fall 2002, Spring 2009, Spring 2012, Spring 2014
Math337 : Introduction to Soliton Theory. An Undergraduate
elective Course.
Text book:
Solitons by P.G. Drazin and R.S. Johnson ,
Cambridge University. London Mathematical
Society Lecture Note Series 85 .
Course Schedule:
Wednesday 13.40-15.30 SA-Z01
Friday 15.40-17.30 SAZ-Z01
Exams:
(%25) First Midterm Exam (2009)
, (2012) : March 21, 2014
(%25) Second Midterm Exam (2009),
(2012) : May 2, 2014
(%26) Final Exam (2009) ,
(2012) :xx,2014
(%24) Homework:
Homework assignments
FZ Grade Policy:
Failure to attend at least 50% of the classes or averaging less than 40%
from the two midterms will result in an FZ grade.
Lectures
Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 5
Subjects Covered
1. 6 February
Dispersion, Dissipiation and nonlinearity
Solitary waves and Solitons
The KdV equation and its solitary waves
Lecture 1
First Homework set
2. 13 February
Symmetries of the KdV equation
Reduction of KdV to ODEs (Group Invariant Solutions)
Travelling wave solutions of KdV
Solutions in terms of Jacobi Elliptic functions
Cnoidal waves , solitary waves
3. 20 February
Group invariant solutions of Burgers Equation
Group invariant solutions of modified Korteweg-de Vries Equation
Group invariant solutuins of Nonlinear Schrodinger Equation
4. 27 February
The scattering problem
Sturm-Liouville eigenvalue problem
Delta function and sech^2 function
(We omitted the section 3.3)
Second Homework set
Lecture 2
5. 5 March
Lax Equations
Time evolution of the scattering data
Solutions of the GLM equation
One and two soliton solutions of the KdV equation
6. 12 March
Lax Formulation
The KdV Hierarchy
Inverse scattering of the KdV Hierarchy
Lecture 3
7. 19 March
First Midterm Exam
Solutions of the first midterm exam
One soliton solution of the KdV hierarchy
Third Homework set
8. 26 March
The Hirota method (for the KdV equation)
9. 2 April
Backlund transformations
Backlund transformations (for the KdV equation)
Fourth Homework set
10. 9 April
Other Backlund transformations
Nonlinear superposition rule (for KdV and SG equations)
Lecture 4
11. 16 April
Fifth Homework set
Variational Calculus
12. 23 April
Hamiltonian formulation of KdV equation
13. 30 April
AKNS Formulation
Lecture 5
Second Midterm Exam(2012)
14. 07 May
Poisson Brackets
Hydrodynamic Type of Integrable Equations
Course Syllabus
1. Sept.23. The Koteweg de Vries Eqiuation
2. Sept.30. The Korteweg de Vries Equation
3. Oct.07. The Cnoidal waves
4. Oct.14. The Cnoidal waves.
5. Oct.21. The Conservation Laws
6. Oct.28. The Conservation Laws
7. Oct.25. The Initial Value problem of the KdV equation
8. Nov.01. The Initial Value problem of the KdV equation
9. Nov.08. The Lax Method
10. Nov.15. The Lax Method
11. Nov.22. Sine Gordon equation
12. Nov.29. Sine Gordon Equation
13. Dec.06. Backlund Transformations
14. Dec.13. Backlund Transformations.
15. Dec.20. AKNS System
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Last update January 2014
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