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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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