Solitons and conservation laws of Klein–Gordon equation with power law and log law nonlinearities

Biswas, Anjan; Kara, A. H.; Bokhari, Ashfaque H.; Zaman, F. D.

doi:10.1007/s11071-013-0933-5

Cited by 52 publications

(25 citation statements)

References 13 publications

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“…Numerous powerful methods have been used to seek the conservation laws: Laplace direct technique [34], characteristic form given by Stuedel [35], q-homotopy analysis transform method (q-HATM) [36], multiplier approach [37,38]. In this thesis, based on the modified CamassaHolm equation [39] and ZK-BBM equations [40] for each multiplier, and the method of Ibragimov (nonlocal conservation method) [41][42][43], using the multiplier approach, conservation laws and the corresponding conserved quantities are discussed.…”

Section: Introductionmentioning

confidence: 99%

Combined ZK-mZK equation for Rossby solitary waves with complete Coriolis force and its conservation laws as well as exact solutions

et al. 2018

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In the present paper, a new partial differential equation has been obtained to describe the Rossby solitary waves with complete Coriolis force by employing multi-scale analysis and perturbation method, we call it combined ZK-mZK equation. The equation can reflect the propagation of Rossby waves on the plane and is more appropriate for the real ocean and atmosphere than the (1 + 1) dimensional models (such as KdV and mKdV), which can only represent the propagation of Rossby solitary waves in a line. Furthermore, by adopting the multiplier method, we construct conservation laws of the combined ZK-mZK equation, which is meaningful for researching the global stability of solutions. Finally, we deduce the exact solutions of the combined ZK-mZK equation via the semi-inverse variational principle. By applying these exact solutions, some propagation features of Rossby solitary waves are analyzed.

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Section: Introductionmentioning

confidence: 99%

Combined ZK-mZK equation for Rossby solitary waves with complete Coriolis force and its conservation laws as well as exact solutions

et al. 2018

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“…In general, Lie symmetries can be used to reduce the order as well number of independent variables of original equation (system of equations). For further details, readers are referred to [1][2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Symmetry analysis and conservation laws for the class of time-fractional nonlinear dispersive equation

2015

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“…Lie's theory provides a useful, powerful tool when analysing partial differential equations. Moreover, it has numerous well-known applications, prominent among these are the obtaining of exact solutions of partial differential equations, directly or via similarity solutions [7,17], classifying invariant equations, reducing the number of independent variables or determining conservation laws [1,2,5,6,14].…”

Section: Introductionmentioning

confidence: 99%

“…We obtain the continuous equivalence transformations of class (1). This allow us to reduce the number of arbitrary elements of class (1) which will result in a complete study of Lie symmetries of class (1). Moreover, we determine the subclasses of the equation, which are quasi self-adjoint and nonlinear self-adjoint.…”

Section: Introductionmentioning

confidence: 99%

Symmetries and conservation laws of a fifth-order KdV equation with time-dependent coefficients and linear damping

2015

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A fifth-order KdV equation with timedependent coefficients and linear damping has been studied. Symmetry groups have several different applications in the context of nonlinear differential equations; for instance, they can be used to determine conservation laws. We obtain the symmetries of the model applying Lie's classical method. The choice of some arbitrary functions of the equation by the equivalence transformation enhances the study of Lie symmetries of the equation. We have determined the subclasses of the equation which are nonlinearly self-adjoint. This allow us to obtain conservation laws by using a theorem proved by Ibragimov which is based on the concept of adjoint equation for nonlinear differential equations.

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Solitons and conservation laws of Klein–Gordon equation with power law and log law nonlinearities

Cited by 52 publications

References 13 publications

Combined ZK-mZK equation for Rossby solitary waves with complete Coriolis force and its conservation laws as well as exact solutions

Combined ZK-mZK equation for Rossby solitary waves with complete Coriolis force and its conservation laws as well as exact solutions

Symmetry analysis and conservation laws for the class of time-fractional nonlinear dispersive equation

Symmetries and conservation laws of a fifth-order KdV equation with time-dependent coefficients and linear damping

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