Abstract
Contrary to the common understanding, the sine-Gordon equation in (1+2) dimensions does have N-soliton solutions for any N. The Hirota algorithm allows for the construction of static N-soliton solutions (i.e., solutions that do not depend on time) of that equation for any N. Lorentz transforming the static solutions yields N-soliton solutions in any moving frame. They are scalar functions under Lorentz transformations. In an N-soliton solution in a moving frame, (N-2) of the (1+2)-dimensional momentum vectors of the solitons are linear combinations of the two remaining vectors.
Original language | English |
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Article number | 013512 |
Journal | Journal of Mathematical Physics |
Volume | 54 |
Issue number | 1 |
DOIs | |
State | Published - 22 Jan 2013 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics