Abstract:A symmetry-based method for constructing nonlocally related partial differential equation systems A family of exact travelling wave solutions to nonlinear evolution and wave equations
“…in the results of [1], the Noether symmetries of the wave equation on static spherically symmetric spacetimes in terms of the functions k 1 ðt; rÞ; k 2 ðt; rÞ; k 7 ðt; rÞ; k 8 ðt; rÞ; k 9 ðt; rÞ and the three constants d 1 ; d 2 ; d 3 can be given as …”
Section: Noether Symmetries Of Wave Eq (12) On Static Spherically Smentioning
confidence: 99%
“…As mentioned in Section 1, the system and the constraints that can be used to determine the Noether symmetries of the wave equation on general spherically symmetric spacetimes were provided in [1]. Introducing the auxiliary function Z ¼ ðk 2 sin / À k 1 cos /Þ sin h À k 7 cos h ð2:1Þ…”
Section: Noether Symmetries Of Wave Eq (12) On Static Spherically Smentioning
confidence: 99%
“…For the case of wave equation on spherically symmetric spacetimes, Bokhari et al [1] provided the Noether symmetries in terms of five functions of the variables t and r subject to certain differential equations and constraints. Here we consider the wave equation on static spherically symmetric spacetimes admitting G 10 or G 7 or G 6 and completely solve the differential equations and constraints of [1] to obtain the corresponding Noether symmetries and conservation laws.…”
Section: Introductionmentioning
confidence: 99%
“…Here we consider the wave equation on static spherically symmetric spacetimes admitting G 10 or G 7 or G 6 and completely solve the differential equations and constraints of [1] to obtain the corresponding Noether symmetries and conservation laws. For references related to the applications and various approaches of obtaining conservation laws, the reader is referred to [9][10][11][12][13].…”
Section: Introductionmentioning
confidence: 99%
“…In Bokhari et al (2011), the Noether symmetries of the wave equation on a general spherically symmetric spacetime metric were provided in terms of five functions of the variables t and r subject to certain differential equations and constraints. In this work, these differential equations and constraints are solved for all the static spherically symmetric spacetimes admitting G 10 or G 7 or G 6 as maximal isometry group.…”
“…in the results of [1], the Noether symmetries of the wave equation on static spherically symmetric spacetimes in terms of the functions k 1 ðt; rÞ; k 2 ðt; rÞ; k 7 ðt; rÞ; k 8 ðt; rÞ; k 9 ðt; rÞ and the three constants d 1 ; d 2 ; d 3 can be given as …”
Section: Noether Symmetries Of Wave Eq (12) On Static Spherically Smentioning
confidence: 99%
“…As mentioned in Section 1, the system and the constraints that can be used to determine the Noether symmetries of the wave equation on general spherically symmetric spacetimes were provided in [1]. Introducing the auxiliary function Z ¼ ðk 2 sin / À k 1 cos /Þ sin h À k 7 cos h ð2:1Þ…”
Section: Noether Symmetries Of Wave Eq (12) On Static Spherically Smentioning
confidence: 99%
“…For the case of wave equation on spherically symmetric spacetimes, Bokhari et al [1] provided the Noether symmetries in terms of five functions of the variables t and r subject to certain differential equations and constraints. Here we consider the wave equation on static spherically symmetric spacetimes admitting G 10 or G 7 or G 6 and completely solve the differential equations and constraints of [1] to obtain the corresponding Noether symmetries and conservation laws.…”
Section: Introductionmentioning
confidence: 99%
“…Here we consider the wave equation on static spherically symmetric spacetimes admitting G 10 or G 7 or G 6 and completely solve the differential equations and constraints of [1] to obtain the corresponding Noether symmetries and conservation laws. For references related to the applications and various approaches of obtaining conservation laws, the reader is referred to [9][10][11][12][13].…”
Section: Introductionmentioning
confidence: 99%
“…In Bokhari et al (2011), the Noether symmetries of the wave equation on a general spherically symmetric spacetime metric were provided in terms of five functions of the variables t and r subject to certain differential equations and constraints. In this work, these differential equations and constraints are solved for all the static spherically symmetric spacetimes admitting G 10 or G 7 or G 6 as maximal isometry group.…”
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