Non-local conservation laws for the equations of the irrotational isentropic plane-parallel gas motion

2012 ◽  
Vol 76 (2) ◽  
pp. 199-204 ◽  
Author(s):  
Yu. A. Chirkunov
Keyword(s):  
Conservation Laws ◽  
Local Conservation ◽  
Plane Parallel ◽  
Non Local

scholarly journals A kinetic decomposition for singular limits of non-local conservation laws

2009 ◽  
Vol 247 (12) ◽  
pp. 3338-3356 ◽  
Author(s):  
Frederike Kissling ◽  
Philippe G. LeFloch ◽  
Christian Rohde
Keyword(s):  
Conservation Laws ◽  
Local Conservation ◽  
Singular Limits ◽  
Kinetic Decomposition ◽  
Non Local

scholarly journals Deformed Sine-Gordon Models, Solitons and Anomalous Charges

2021 ◽  
Author(s):  
Harold Blas ◽  
Hector F. Callisaya ◽  
João P.R. Campos ◽  
Bibiano M. Cerna ◽  
Carlos Reyes
Keyword(s):  
Conservation Laws ◽  
Infinite Number ◽  
Soliton Solutions ◽  
Linear Formulation ◽  
Reflection Symmetry ◽  
Local Conservation ◽  
Time Symmetry ◽  
Non Local ◽  
Sine Gordon Model ◽  
Special Space

We study certain deformations of the integrable sine-Gordon model (DSG). It is found analytically and numerically several towers of infinite number of anomalous charges for soliton solutions possessing a special space–time symmetry. Moreover, it is uncovered exact conserved charges associated to two-solitons with a definite parity under space-reflection symmetry, i.e. kink-kink (odd parity) and kink-antikink (even parity) scatterings with equal and opposite velocities. Moreover, we provide a linear formulation of the modified SG model and a related tower of infinite number of exact non-local conservation laws. We back up our results with extensive numerical simulations for kink-kink, kink-antikink and breather configurations of the Bazeia et al. potential V q w = 64 q 2 tan 2 w 2 1 − sin w 2 q 2 , q ∈ R , which contains the usual SG potential V 2 w = 2 1 − cos 2 w .

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