Small changes can alter the nature of the nodal set
Chapter 10, Problem 3(choose chapter or problem)
Small changes can alter the nature of the nodal set drastically. Use a computer program to show that the eigenfunction sin 12x sin y + sin x sin 12y has a nodal set that divides the square (0, )2 into 12 subregions, butthattheeigenfunctionsin12x siny+ sinx sin12y,for near1,has a nodal set that divides it into only two subregions. Show that the nodal sets are as sketched in Figure 2.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer