Phys. Rev. Lett. 58, 747–750 (1987)Nonexistence of small-amplitude breather solutions in phi4 theorySee Also: Erratum Received 1 August 1986; published in the issue dated 23 February 1987 For the (1+1)-dimensional Klein-Gordon equation called the φ4 model, there is a known asymptotic series formally representing a ‘‘breather’’ (a real-valued solution that is localized in space and periodic in time) in the limit of small amplitude and frequency just below that of spatially uniform infinitesimal oscillations. We show that even though this expansion is valid to all orders, φ4 theory admits no true breathers in this limit. Instead, what appear in many physical contexts are approximate breathers that slowly radiate their energy to x-±∞. We calculate this radiation rate, which lies beyond all orders in the asymptotic expansion. © 1987 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.58.747
DOI:
10.1103/PhysRevLett.58.747
PACS:
03.50.-z, 02.30.+g, 42.65.Bp, 63.10.+a
See AlsoComment: Yuri S. Kivshar and Boris A. Malomed, Comment on "Nonexistence of Small-Amplitude Breather Solutions in φ4 Theory", Phys. Rev. Lett. 60, 164 (1988). Erratum: Harvey Segur and Martin D. Kruskal, Nonexistence of Small-Amplitude Breather Solutions in φ4 Theory, Phys. Rev. Lett. 58, 1158 (1987). |
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