I need to understand the basic difference between the two integrable models given below.
same signs of dispersion and interaction strengths in Manakov model
1q_{i}t + q_{i}xx+2(|q_{i}|^2 +|q_{j}|)q_{i}=0 where i,j=1,2
Opposite signs of dispersion and interaction strengths in Manakov model
1q_{i}t - q_{i}xx+2(|q_{i}|^2 +|q_{j}|)q_{i}=0 where i,j=1,2
Kindly do clarify....
A. J. Roberts
Well one difference is that the first is only stable if you integrate backwards in time, whereas the second is only stable if you integrate forwards in time. Is that the sort of comment you are looking for?
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Roman Taranets
For understanding difference, you need solve more simple equations
u_t - u_{xx} = 0 stable diffusion
and
u_t + u_{xx} = 0 unstable diffusion
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