1. Asymptotic Nonlinearities in Smectics
E.A. Brener

2. Dislocations in smectics

3. The elastic energy of smectics
Equation of equilibrium

4. Green’s functions

5. the linear theory is valid
Scaling relations
For
the linear theory is valid

6. transition takes place at
Shear deformation
far from the wall
near the wall
transition takes place at

7. Force applied along the z axis
Far from the defect line one can neglect bending energy and displacement is At
transition to the linear theory u~
takes place

8. Dislocations in smectics

9. Dislocations in smectics
Linear theory (de Gennes)
Nonlinear theory (Brener and Marchenko) At
the result of the linear theory is recovered

10. Details of solution is the solution of the original 3rd order equation
subject to the constraint
is the solution of the original 3rd order equation

11. “Nonlinear” Green’s function
In the linear approximation

12. Equation can be reduced to
Details of solution
Equation can be reduced to

13. Numerical solution of the equation

14. Strongly nonlinear regime,