Lecture 2.10: FOPDE's- General nonlinear equations 1 - Search for a characteristic direction
Channel: IIT Bombay July 2018
Date: 2021-08-05

In this lecture, we will begin studying general nonlinear equations. Motivated by the method of solutions for quasilinear equations, we will search for a characteristic direction for general nonlinear equations, which will lead us to look at the theory of envelopes
(1) Please note the following corrections to Slide 35:
     (a) Replace ``Plus or Minus sign'' in equation (9) with ``Plus''. 
     (b) In the fraction on RHS of equation (9), change the numerator from  
      ``1"  to "|x|" . This means that we are considering positive values for p.
 
(2) Please note the following corrections to Slide 36:
      (a) Remove the condition ``|z| greater than 1'' in equation
           (10) . 
      (b) Equation (10) is the equation of the envelope for (x,y) in the first and
            third quadrants, as we used that |x|=x and |y|=y in arriving at the 
            equation (10). Of course, equation of the envelope may be found in 
             the other quadrants.

(3) Figure on Slide 37 should be understood with the modifications in (2) 
     above. In other words, the figure is relevant only for (x,y) in the first and
     third quadrants.