Wave equation on spherically symmetric Lorentzian metrics

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

Noether symmetries and conservation laws of wave equation on static spherically symmetric spacetimes with higher symmetries

“…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 …”

“…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…”

“…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.…”

“…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].…”

“…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.…”