Continuous vacua in bilinear soliton equations

Details Continuous vacua in bilinear soliton equations Continuous vacua in bilinear soliton equations

1993-11-24

arxiv.org/abs/solv-int/9311001v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages in Latex + 3 figures (not included)

Scientific paper

10.1088/0305-4470/27/9/027

We discuss the freedom in the background field (vacuum) on top of which the solitons are built. If the Hirota bilinear form of a soliton equation is given by $A(D_{\vec x})\bd GF=0,\, B(D_{\vec x})(\bd FF - \bd GG)=0$ where both $A$ and $B$ are even polynomials in their variables, then there can be a continuum of vacua, parametrized by a vacuum angle $\phi$. The ramifications of this freedom on the construction of one- and two-soliton solutions are discussed. We find, e.g., that once the angle $\phi$ is fixed and we choose $u=\arctan G/F$ as the physical quantity, then there are four different solitons (or kinks) connecting the vacuum angles $\pm\phi$, $\pm\phi\pm\Pi2$ (defined modulo $\pi$). The most interesting result is the existence of a ``ghost'' soliton; it goes over to the vacuum in isolation, but interacts with ``normal'' solitons by giving them a finite phase shift.

Affiliated with

Also associated with

No associations

Rating

Continuous vacua in bilinear soliton equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Continuous vacua in bilinear soliton equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Continuous vacua in bilinear soliton equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-501881