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TMF, 1976, Volume 29, Number 2, Pages 213–220 (Mi tmf3452)  

This article is cited in 6 scientific papers (total in 6 papers)

Application of the inverse scattering method to the equation $\sigma_{xt}=e^\sigma$

V. A. Andreev


Abstract: It is shown that the equation $\sigma_{xt}=e^\sigma$, which arises in many branches of physics and mathematics, can be exactly solved by means of the inverse scattering problem. Here, $N$-soliton solutions are constructed. These solutions describe one movIng soliton and $N-1$ fixed solitons. The phase shift of the moving soliton resulting from scattering on fixed solitons is found. Conservation laws are constructed. The method used in the paper differs somewhat from the ordinary method of the inverse scattering problem.

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English version:
Theoretical and Mathematical Physics, 1976, 29:2, 1027–1032

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Received: 18.02.1976

Citation: V. A. Andreev, “Application of the inverse scattering method to the equation $\sigma_{xt}=e^\sigma$”, TMF, 29:2 (1976), 213–220; Theoret. and Math. Phys., 29:2 (1976), 1027–1032

Citation in format AMSBIB
\Bibitem{And76}
\by V.~A.~Andreev
\paper Application of the inverse scattering method to the equation $\sigma_{xt}=e^\sigma$
\jour TMF
\yr 1976
\vol 29
\issue 2
\pages 213--220
\mathnet{http://mi.mathnet.ru/tmf3452}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=447845}
\transl
\jour Theoret. and Math. Phys.
\yr 1976
\vol 29
\issue 2
\pages 1027--1032
\crossref{https://doi.org/10.1007/BF01108506}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. M. Barbashov, V. V. Nesterenko, A. M. Chervyakov, “Solitons in some geometrical field theories”, Theoret. and Math. Phys., 40:1 (1979), 572–581  mathnet  crossref  mathscinet  isi
    2. G. P. Jorjadze, A. K. Pogrebkov, M. K. Polivanov, “Singular solutions of the equation $\Box\varphi+(m^2/2)\exp\varphi=0$ and dynamics of singularities”, Theoret. and Math. Phys., 40:2 (1979), 706–715  mathnet  crossref  mathscinet  zmath  isi
    3. G. P. Jorjadze, “Regular solutions of the Liouville equation”, Theoret. and Math. Phys., 41:1 (1979), 867–871  mathnet  crossref  mathscinet  zmath  isi
    4. V. A. Andreev, M. V. Burova, “Lower Korteweg–de Vries equations and supersymmetric structure of the sine-Gordon and Liouville equations”, Theoret. and Math. Phys., 85:3 (1990), 1275–1283  mathnet  crossref  mathscinet  zmath  isi
    5. B. Fuchssteiner, V. V. Tsegel'nik, “Analytical properties of solutions to a system of nonlinear partial differential equations”, Theoret. and Math. Phys., 105:2 (1995), 1354–1358  mathnet  crossref  mathscinet  zmath  isi
    6. V. A. Andreev, “System of equations for stimulated combination scattering and the related double periodic $A_n^{(1)}$ Toda chains”, Theoret. and Math. Phys., 156:1 (2008), 1020–1027  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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