General formulas for solutions of initial and boundary-value problems for the sine-Gordon equation

1995 ◽  
Vol 103 (3) ◽  
pp. 613-620 ◽  
Author(s):  
E. D. Belokolos
Keyword(s):  
Boundary Value Problems ◽  
Gordon Equation ◽  
Boundary Value ◽  
Sine Gordon Equation

scholarly journals Boundary Value Problems for the Elliptic Sine-Gordon Equation in a Semi-strip

2012 ◽  
Vol 23 (2) ◽  
pp. 241-282 ◽  
Author(s):  
A. S. Fokas ◽  
J. Lenells ◽  
B. Pelloni
Keyword(s):  
Boundary Value Problems ◽  
Gordon Equation ◽  
Boundary Value ◽  
Sine Gordon Equation

scholarly journals On the Lie symmetries of the boundary value problems for differential and difference sine-Gordon equations

2021 ◽  
Vol 102 (2) ◽  
pp. 142-153
Author(s):  
O. Yildirim ◽  
◽  
S. Caglak ◽  
Keyword(s):  
Group Theory ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Gordon Equation ◽  
Boundary Value ◽  
Lie Point Symmetries ◽  
Sine Gordon Equation ◽  
Difference Problem ◽  
Lie Group Theory ◽  
The Difference

In general, due to the nature of the Lie group theory, symmetry analysis is applied to single equations rather than boundary value problems. In this paper boundary value problems for the sine-Gordon equations under the group of Lie point symmetries are obtained in both differential and difference forms. The invariance conditions for the boundary value problems and their solutions are obtained. The invariant discretization of the difference problem corresponding to the boundary value problem for sine-Gordon equation is studied. In the differential case an unbounded domain is considered and in the difference case a lattice with points lying in the plane and stretching in all directions with no boundaries is considered.

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