Abstract
An equation originally derived from non-relativistic ideal gasdynamics turns out to be reducible to a Lorentz invariant nonlinear version of the Klein-Gordon equation. We present its interacting soliton solutions, which are here constructed by means of a Bäcklund transformation, starting from the “vacuum”.
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I was not aware of MIkhailov's (34) work on the equation: ρtt − ρxx + 2eρ4ρ − 2e−ρ = 0 until the present work has been completed. In particular, Mikhailov shows that the equation is completely integrable and can be solved by a third-order Inverse Scattering Transform. An infinite number of polynomial conserved densities has also been found to exist.
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Gaffet, B. (1988). An SL(3)-Symmetrical F-Gordon equation:ZαB = 1/3 (eZ−e−2Z). In: de Vega, H.J., Sánchez, N. (eds) Field Theory, Quantum Gravity and Strings. Lecture Notes in Physics, vol 246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16452-9_19
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DOI: https://doi.org/10.1007/3-540-16452-9_19
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