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Article
Open AccessOn first integrals, conservation laws and reduction of classes of Emden and Liénard equations
We present a general method to construct first integrals for some classes of the well known second-order ordinary differential equations, viz., the Emden and Liénard classes of equations. The approach does not...
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Article
New Exact Solutions of the Thomas Equation Using Symmetry Transformations
Lie symmetry analysis of differential equations is one of the most effective techniques to find exact solutions to a differential equation or to reduce the number of independent variables or at least reduce th...
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Article
Explicit exact solutions and conservation laws in a medium with competing weakly nonlocal nonlinearity and parabolic law nonlinearity
In this paper, we studied a nonlinear wave equation that models the propagation of optical solutions in a weakly nonlocal and parabolic competing nonlinear medium. The exact traveling wave type solutions formu...
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Article
Conservation laws and solution of the geodesic system of Gödel’s metric via Lie and Noether symmetries
We consider the geodesic system for Gödel’s metric as a toy model and solve it analytically using its Lie point symmetries. It is shown that the differential invariants of these symmetries reduce the second-or...
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Article
The relativistic heat equation on flat Friedman spacetime
The exact solutions of the relativistic hyperbolic heat equation on a flat Friedman spacetime metric are obtained. These solutions are obtained in three cases of flat Friedman model which correspond to radiati...
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Article
Image Processing and ‘Noise Removal Algorithms’—The Pdes and Their Invariance Properties & Conservation Laws
We analyse the symmetry, invariance properties and conservation laws of the partial differential equations (pdes) and minimization problems (variational functionals) that arise in the analyses of some noise re...
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Article
Wave equations on anti self dual (ASD) manifolds
In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric \(g_{ij}\) ...
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Article
Symmetry and conservation law structures of some anti-self-dual (ASD) manifolds
The ASD systems and manifolds have been studied via a number of approaches and their origins have been well documented. In this paper, we look at the symmetry structures, variational symmetries and related con...
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Article
Nonlocal symmetry analysis and conservation laws to an third-order Burgers equation
The nonlocal residual symmetry related to truncated Painlevé expansion of third-order Burgers equation is performed. Then, the potential symmetries of the equation are derived; on the basis of nonlocal symmetr...
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Article
An analysis of the Zhiber-Shabat equation including Lie point symmetries and conservation laws
We address the integrability aspects of the Zhiber-Shabat equation that serves as a generalised version of the \(\Phi -4\) ...
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Article
Symmetry analysis and conservation laws for the class of time-fractional nonlinear dispersive equation
In this paper, we derive the complete algebra of Lie point symmetries for the class of time-fractional nonlinear dispersive equation. By means of the classical Lie symmetry method, the associated vector fields...
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Article
Conservation laws, multipliers, adjoint equations and Lagrangians for Jaulent–Miodek and some families of systems of KdV type equations
In this paper, we will show and integrate the ‘multiplier’ and ‘adjoint equations and Lagrangian’ approaches to the construction of conservation laws. The details will reveal how the method lends itself to hig...
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Article
Symmetry structure of a wave equation on some classes of Bianchi cosmological models
Nonlinear wave equations are constructed on certain Bianchi models and a symmetry analysis of these equations are performed to construct some exact solutions. Conservation laws of the respective wave equations...
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Article
On the Reduction of Some Dispersionless Integrable Systems
We study the invariance, reduction, exact solutions and conservation laws of the dispersionless Kadomtsev-Petviashivili and the heavenly equation. The existence of nontrivial conservation laws lead to repeated...
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Article
Domain walls to Boussinesq-type equations in (2 + 1)-dimensions
In this paper, two models with fourth-order dispersion in 2 + 1 dimensions are investigated. Based on Ansatz method, exact domain wall solutions are derived. Parametric conditions for the existence of the doma...
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Article
Invariances and Conservation Laws Based on Some FRW Universes
A symmetry analysis of some special classes of Friedmann-Robertson-Walker (FRW) universe and nonlinear wave equations in this geometry are performed. Conserved forms for the wave equation are constructed by th...
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Article
Solitary waves and conservation laws of complex-valued Klein–Gordon equation in \(\Upphi\) -4 field theory
In this paper, the ansatz method is used to obtain solitary wave solution, topological solitary wave solution and singular solitary wave solution of the complex valued Klein–Gordon equation with power law nonl...
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Article
Topological solitons, cnoidal waves and conservation laws of coupled wave equations
In this paper a few coupled wave equations that arise in the dynamics of two-layered shallow water waves in ocean shores and beaches have been studied. The map** method is applied to extract cnoidal waves an...
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Article
Proper projective symmetry in Bianchi type I space-times
A study of the most general form of Bianchi type I space-times is given by using the direct integration and algebraic techniques. In this study we deal with the cases where all the eigenvalues of the Riemann t...
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Article
Classification of Static Spherically Symmetric Spacetimes by Noether Symmetries
Noether symmetries of some of the well known spherically symmetric static solutions of the Einstein’s field equations are classified. The resulting Noether symmetries in each case are compared with conservatio...
