Forced Integrable Systems - The Case of Sine-Gordon Equation by Vasudeva Murthy

Forced Integrable Systems - The Case of Sine-Gordon Equation by Vasudeva Murthy

International Centre for Theoretical Sciences via YouTube Direct link

Theory

18 of 23

18 of 23

Theory

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Forced Integrable Systems - The Case of Sine-Gordon Equation by Vasudeva Murthy

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  1. 1 Forced integrable systems: the case of sine-Gordon equation
  2. 2 Revisiting the inhomogeneously driven sine-Gordon equation
  3. 3 Dynamics of a one-dimensional crack with variable friction
  4. 4 Linear stress-drop model
  5. 5 Sine-Gordon equation and its application to tectonic stress transfer
  6. 6 Dynamics of a one-dimensional crack
  7. 7 Figure 2: Solution of inhomogeneous sG equation with constant and Heaviside forcing for different times
  8. 8 Kink with No Flux Boundary Conditions:
  9. 9 Kink with Non-reflecting Boundary Conditions:
  10. 10 Acritical vs C Variation over different domain size
  11. 11 Breather with Non-Reflecting Boundary Conditions:
  12. 12 Breather with No Flux Boundary Conditions:
  13. 13 Variation of Acritical with C:
  14. 14 Conclusions
  15. 15 Future?
  16. 16 Finite Difference Methods for the heat Equation with a Nonlocal Boundary Condition
  17. 17 Nonlinear problems?
  18. 18 Theory
  19. 19 Keller & Hagstrom 1986
  20. 20 The technique
  21. 21 Need to do the same for the sine-Gordon equation
  22. 22 The Generalized Dirichlet-to-Neumann Map for Certain Nonlinear Evolution PDFs
  23. 23 Q&A

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