Nonautonomous soliton solutions of the modified Korteweg–de Vries–sine-Gordon equation

2016 ◽  
Vol 56 (11) ◽  
pp. 1929-1937
Author(s):  
S. P. Popov
Keyword(s):  
Gordon Equation ◽  
Soliton Solutions ◽  
Sine Gordon Equation ◽  
De Vries ◽  
Nonautonomous Soliton

Corrigenda

1978 ◽  
Vol 362 (1711) ◽  
pp. 572-572
Keyword(s):  
Gordon Equation ◽  
Soliton Solutions ◽  
Sine Gordon Equation ◽  
Multiple Soliton Solutions

Proc. R. Soc. Lond . A 359, 479-495 (1978) Exact, multiple soliton solutions of the double sine Gordon equation By P. G. Burt Equation (A 10), exponent of P should read - 1/(2 p ). Equation (A 15), exponents of P should read - 1/(2 p ) and - (1/(2 p ) + 1) respectively. Proc. R. Soc. Lond . A 362, 281-303 (1978) The Bakerian Lecture, 1977: in vitro models for photosynthesis By Sir George Porter, F. R. S. Page 300, line —8: for λ < 455 nm read λ > 455 nm

scholarly journals Darboux transformation and multi-soliton solutions of the discrete sine-Gordon equation

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
Y Hanif ◽  
U Saleem
Keyword(s):  
Darboux Transformation ◽  
Gordon Equation ◽  
Soliton Solutions ◽  
Sine Gordon Equation ◽  
Dynamical Features ◽  
Discrete Darboux Transformation ◽  
Explicit Expressions

Abstract We study the discrete Darboux transformation and construct multi-soliton solutions in terms of the ratio of determinants for the integrable discrete sine-Gordon equation. We also calculate explicit expressions of single-, double-, triple-, and quadruple-soliton solutions as well as single- and double-breather solutions of the discrete sine-Gordon equation. The dynamical features of discrete kinks and breathers are also illustrated.

Integrable and solvable systems, and relations among them

1985 ◽  
Vol 315 (1533) ◽  
pp. 451-457 ◽  
Keyword(s):  
Gordon Equation ◽  
Soliton Solutions ◽  
The Self ◽  
Sine Gordon Equation ◽  
Field Equations ◽  
Four Dimensions ◽  
Painlevé Property ◽  
All Solutions ◽  
Special Cases ◽  
Integrable Dynamical Systems

There are several different classes of differential equations that may be described as ‘integrable’ or ‘solvable’. For example, there are completely integrable dynamical systems; equations such as the sine—Gordon equation, which admit soliton solutions; and the self-dual gauge-field equations in four dimensions (with generalizations in arbitrarily large dimension). This lecture discusses two ideas that link all of these together: one is the Painlevé property, which says (roughly speaking) that all solutions to the equations are meromorphic; the other is that many of the equations are special cases (i.e. reductions) of others.

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