Homework Assignment 2
 

1.     In the process of  deriving the  KdV equation as the limit of  a lattice model, the equation

                   u_tt =  c²u_xx  +  h²(c² u_xxxx +  a  u_xx(u_x))

is found.   Find the solitons of this equation, and show that they will transfer to the solitons of the KdV equation under the limiting
process.
 

2.   Do problem 2.1, or  find the formula for A which is discussed in the lecture for the interaction of two solitons.