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

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

Bibliographic databases:

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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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
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
3. G. P. Jorjadze, “Regular solutions of the Liouville equation”, Theoret. and Math. Phys., 41:1 (1979), 867–871
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
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
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
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