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We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the electromagnetic field. New exact solutions are found to the Einstein-Maxwell system. A particular case is shown to be regular at the stellar centre. In the isotropic limit...
In this paper, we show the applicability of the first integral method to combined KdV–mKdV equation, Pochhammer–Chree equation and coupled nonlinear evolution equations. The power of this manageable method is confirmed by applying it for three selected nonlinear evolution equations. This approach can also be applied to other nonlinear differential equations.
In this paper, we implemented the functional variable method for the exact solutions of the Zakharov–Kuznetsov-modified equal-width (ZK-MEW), the modified Benjamin–Bona–Mahony (mBBM) and the modified KdV–Kadomtsev–Petviashvili (KdV–KP) equations. By using this scheme, we found some exact solutions of the above-mentioned equations. The obtained solutions include solitary wave solutions, periodic wave...
In this paper, we obtain the 1-soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and the generalized Benjamin equation. By using two solitary wave ansatz in terms of sechp and functions, we obtain exact analytical bright and dark soliton solutions for the considered model. These solutions may be useful and desirable for explaining some...
In this paper, we implemented the functional variable method and the modified Riemann–Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the time-fractional Klein–Gordon equation, and the time-fractional Hirota–Satsuma coupled KdV system. This method is extremely simple but effective for handling nonlinear time-fractional differential equations.
The modified multiple ( G ′ / G )-expansion method is proposed in this paper to construct exact solutions of nonlinear evolution equations. The validity and advantage of the proposed method are illustrated by its application to the Sharma–Tasso–Olver equation. As a result, various exact solutions including hyperbolic functions, trigonometric functions and their mixture with...
In this paper, the classical Lie group method is employed to obtain exact travelling wave solutions of the generalized Camassa–Holm Kadomtsev–Petviashvili (g-CH–KP) equation. We give the conservation laws of the g-CH–KP equation. Using the symmetries, we find six classical similarity reductions of g-CH–KP equation. Many kinds of exact solutions of the g-CH–KP equation are derived by solving the reduced...
In this paper we show that the Darboux transformation for a large class of nonlinear evolution equations arises due to factorization and commutation. The factorization and commutation has been pointed out earlier for Schrödinger operator. We show that it extends to a large class of nonlinear differential equations which admit Lax pairs including Boussinesq, Davey–Stewartson, Bogoyavlensky–Schiff and...
A new solution of Einstein’s vacuum field equations is discovered which appears as a generalization of the well-known Ozsváth–Schücking solution and explains its source of curvature which has otherwise remained hidden. Curiously, the new solution has a vanishing Kretschmann scalar and is singularity-free despite being curved. The discovery of the new solution is facilitated by a new insight which...
The charged anisotropic star on paraboloidal space-time is reported by choosing a particular form of radial pressure and electric field intensity. The non-singular solution of Einstein–Maxwell system of equation has been derived and it is shown that the model satisfies all the physical plausibility conditions. It is observed that in the absence of electric field intensity, the model reduces to a particular...
Fin materials can be observed in a variety of engineering applications. They are used to ease the dissipation of heat from a heated wall to the surrounding environment. In this work, we consider a nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient. The equation(s) under study are highly nonlinear. Both the thermal conductivity and the heat transfer...
In this article, effects of heat transfer on particle–fluid suspension induced by metachronal wave have been examined. The influence of magnetohydrodynamics (MHD) and thermal radiation are also taken into account with the help of Ohm’s law and Roseland’s approximation. The governing flow problem for Casson fluid model is based on continuity, momentum and thermal energy equation for fluid phase and...
In this paper, we present a formalism to generate a family of interior solutions to the Einstein–Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner–Nordström space–time. By reducing the Einstein–Maxwell system to a recurrence relation with variable rational coefficients, we show that it is possible to obtain closed-form solutions...
The degenerate coupled multi-Korteweg–de Vries equations for coupled multiplicity $$l=3$$ l=3 are studied. The equations, also known as three-field Kaup–Boussinesq equations, are considered for invariant analysis and conservation laws. The classical Lie’s symmetry method is used to analyse the symmetries of equations. Based on the Killing’s form, which is invariant of adjoint action, the full classification...
In this paper, we apply three different techniques, namely, the sine–cosine method, the new extended auxiliary equation method and the modified simple equation method for constructing many new exact solutions with parameters as well as bright–dark, singular and other soliton solutions of the coupled nonlinear Schrödinger equations. The solutions of these coupled nonlinear equations are compared with...
Casson fluid flow has numerous functional applications in food processing, metallurgy, drilling and bio-engineering operations. The significance of Casson fluid in cylindrical coordinates has recently attracted researchers because of the numerical and experimental analyses of the fluid. Due to the lack of fractional analytical approaches, this paper is trying to examine the magnetic effect and thermal...
This paper investigates the new coupled $$(2+1)$$ (2+1) -dimensional Zakharov–Kuznetsov (ZK) system with time-dependent coefficients for multiple types of exact solutions by using the Lie symmetry transformation method. Similarity transformation reduces the system of equations into ordinary differential equations and further, these are solved for solutions having bright, dark and singular solitons...
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