1 research outputs found
Young diagrams and N-soliton solutions of the KP equation
We consider -soliton solutions of the KP equation,
(-4u_t+u_{xxx}+6uu_x)_x+3u_{yy}=0 . An -soliton solution is a solution
which has the same set of line soliton solutions in both
asymptotics and . The -soliton solutions include
all possible resonant interactions among those line solitons. We then classify
those -soliton solutions by defining a pair of -numbers with , which labels line solitons in the solution. The
classification is related to the Schubert decomposition of the Grassmann
manifolds Gr, where the solution of the KP equation is defined as a
torus orbit. Then the interaction pattern of -soliton solution can be
described by the pair of Young diagrams associated with . We also show that -soliton solutions of the KdV equation obtained by
the constraint cannot have resonant interaction.Comment: 22 pages, 5 figures, some minor corrections and added one section on
the KdV N-soliton solution