Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance

2018 ◽  
Vol 505 ◽  
pp. 871-879 ◽  
Author(s):  
Chaudry Masood Khalique ◽  
Tanki Motsepa
Keyword(s):  
Conservation Laws ◽  
Mathematical Finance ◽  
Lie Symmetries ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Group Invariant Solutions

scholarly journals Some symmetries, similarity solutions and various conservation laws of a type of dispersive water waves

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yufeng Zhang ◽  
Na Bai ◽  
Hongyang Guan
Keyword(s):  
Conservation Laws ◽  
Water Waves ◽  
Water Wave ◽  
Wave Equations ◽  
Similarity Solutions ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Lie Transformation ◽  
Group Invariant Solutions ◽  
Special Solutions

Abstract We investigate the point symmetries, Lie–Bäcklund symmetries for a type of dispersive water waves. We obtain some Lie transformation groups, various group-invariant solutions, and some similarity solutions. Besides, we produce different formats of conservation laws of the dispersive water waves by using different schemes. Finally, we consider some special solutions of the stationary dispersive water-wave equations.

scholarly journals Some invariant solutions and conservation laws of a type of long-water wave system

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiangzhi Zhang ◽  
Yufeng Zhang
Keyword(s):  
Conservation Laws ◽  
Water Wave ◽  
Lax Pair ◽  
Wave System ◽  
Series Solutions ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Generalized System ◽  
Group Invariant Solutions ◽  
Similarity Reductions

AbstractWe propose a generalized long-water wave system that reduces to the standard water wave system. We also obtain the Lax pair and symmetries of the generalized shallow-water wave system and single out some their similarity reductions, group-invariant solutions, and series solutions. We further investigate the corresponding self-adjointness and the conservation laws of the generalized system.

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