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

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Teoreticheskaya i Matematicheskaya Fizika, 1976, Volume 29, Number 2, Pages 213–220 (Mi tmf3452)

This article is cited in 20 scientific papers (total in 20 papers)

Application of the inverse scattering method to the equation

σ_{x t} = e^{σ}

$\sigma_{xt}=e^\sigma$

V. A. Andreev

Full-text PDF (766 kB) Citations (20)

References:

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Abstract: It is shown that the equation

σ_{x t} = e^{σ}

$\sigma_{xt}=e^\sigma$ , which arises in many branches of physics and mathematics, can be exactly solved by means of the inverse scattering problem. Here,

N

$N$ -soliton solutions are constructed. These solutions describe one movIng soliton and

N - 1

$N-1$ 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.

Received: 18.02.1976

English version:
Theoretical and Mathematical Physics, 1976, Volume 29, Issue 2, Pages 1027–1032
DOI: https://doi.org/10.1007/BF01108506

Bibliographic databases:

Language: Russian

Citation: V. A. Andreev, “Application of the inverse scattering method to the equation

σ_{x t} = e^{σ}

$\sigma_{xt}=e^\sigma$ ”, TMF, 29:2 (1976), 213–220; Theoret. and Math. Phys., 29:2 (1976), 1027–1032

Citation in format AMSBIB

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\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://mathscinet.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}

Linking options:

https://www.mathnet.ru/eng/tmf3452

https://www.mathnet.ru/eng/tmf/v29/i2/p213

This publication is cited in the following 20 articles:

Lei Cao, Shouxin Chen, “An existence theorem for generalized Abelian Higgs equations and its application”, Proc. R. Soc. A., 480:2298 (2024)
Lei Cao, Shouxin Chen, Yisong Yang, “Domain Wall Solitons Arising in Classical Gauge Field Theories”, Commun. Math. Phys., 369:1 (2019), 317
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
O.K. Pashaev, Jyh-Hao Lee, “Chern–Simons solitons in quantum potential”, Chaos, Solitons & Fractals, 11:14 (2000), 2193
V. M. Eleonsky, V. G. Korolev, “Isospectral deformation of quantum potentials and the Liouville equation”, Phys. Rev. A, 55:4 (1997), 2580
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
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
F. Calogero, A. Degasperis, Order and Chaos in Nonlinear Physical Systems, 1988, 63
Antoine Bredimas, “N-dimensional general solutions of the Liouville type equation with applications”, Physics Letters A, 122:6-7 (1987), 283
G P Jorijadze, A K Pogrebkov, M C Polivanov, S V Talalov, “Liouville field theory: IST and Poisson bracket structure”, J. Phys. A: Math. Gen., 19:1 (1986), 121
L. Bos, R.J. Torrence, “Comment on the Liouville equation and multisolitons”, Physics Letters A, 111:3 (1985), 95
K. Kobayashi, “Nonlinear Klein-Gordon Equations for the Motion of the String”, Progress of Theoretical Physics, 71:2 (1984), 424
E. D'Hoker, R. Jackiw, “Classical and quantal Liouville field theory”, Phys. Rev. D, 26:12 (1982), 3517
Studies in Mathematics and Its Applications, 13, Spectral Transform and Solitons - Tools to Solve and Investigate Nonlinear Evolution Equations, 1982, 488
S.A. Bulgadaev, “Two-dimensional integrable field theories connected with simple lie algebras”, Physics Letters B, 96:1-2 (1980), 151
B. M. Barbashov, V. V. Nesterenko, “Differential Geometry and Nonlinear Field Models”, Fortschr. Phys., 28:8-9 (1980), 427
B. M. Barbashov, V. V. Nesterenko, A. M. Chervyakov, “Solitons in some geometrical field theories”, Theoret. and Math. Phys., 40:1 (1979), 572–581
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
G. P. Jorjadze, “Regular solutions of the Liouville equation”, Theoret. and Math. Phys., 41:1 (1979), 867–871
M. Chaichian, P.P. Kulish, “On the method of inverse scattering problem and Bäcklund transformations for supersymmetric equations”, Physics Letters B, 78:4 (1978), 413

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

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