Solutions for the combined sinh-cosh-Gordon equation

Marin-Ramirez, Ana-Magnolia; Jaramillo-Camacho, Veronica-Patricia; Ortiz-Ortiz, Ruben-Dario

doi:10.12988/ijma.2015.5256

Cited by 4 publications

(3 citation statements)

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“…The modified Liouville equation (Abdelrahman et al, 2015;Salam et al, 2012) plays an important role in various areas of mathematical physics, from plasma physics and field theoretical modeling to fluid dynamics, using various transformations the differential equation can be written as a dynamic system that under some conditions does not have periodic orbits 2013a;Osuna and Villaseñor, 2011). The system in (Marin-Ramirez et al, 2015) coincides to our system. A generalization of a dynamical system was made in (Yan-Min et al, 2016;Qiu-Peng et al, 2015;Xiangwei et al, 2016).…”

Section: Introductionmentioning

confidence: 95%

A Generalization of the Modified Liouville Equation

Rovira-Florián¹,

Marin-Ramirez²,

Ortiz-Ortiz³

2016

American Journal of Applied Sciences

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Section: Introductionmentioning

confidence: 95%

A Generalization of the Modified Liouville Equation

Rovira-Florián¹,

Marin-Ramirez²,

Ortiz-Ortiz³

2016

American Journal of Applied Sciences

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“…Long Wei [23] find out some new type exact solutions for the combined sinh-cosh-Gordon equation based on the a transformed Painlevé property and the variable separated ODE method. The combined sinh-cosh-Gordon equation is also solved by Jaramillo-Camacho and his co-researchers [24] through the Hamiltonnian systems. Magalakwe et al [25] studied a generalized double combined sinh-cosh-Gordon equation by employing Lie group method along with the simplest equation method to search new travelling wave solutions.…”

Section: Introductionmentioning

confidence: 99%

New exact solutions of the combined and double combined sinh-cosh-Gordon equations via modified Kudryashov method

Joardar¹,

Kumar²,

Woadud³

2018

IJPR

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The combined and double combined sinh-cosh-Gordon equations are very important to a wide range of various scientific applications that ranges from chemical reactions to water surface gravity waves. In this article, with the assistance of a function transform and Painlevè property, the nonlinear combined and double combined sinh-cosh-Gordon equations turn into ordinary differential equations. Later on, modified Kudryashov method is adopted for investigating new analytical solution of the studied equations. As a consequence, a series of new analytical solutions are acquired and we demonstrated the actual behavior of the achieved solutions of the mentioned equations with the aid of 3D and 2D MATLAB graphs. Finally, we also validate the effectiveness of the modified Kudryashov method for the problem of extracting new exact solutions of the combined and double combined sinh-cosh-Gordon equations with the aid of Maple package program. It is shown that the implemented method is capable to extract new solutions and it can also use to other nonlinear partial differential equation (NLPDE's) arising in mathematical physics or other applied field.

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“…In [9] it was found a Dulac function for a quadratic system. In [10] was based on finding solutions for the combined sinh-cosh-Gordon equation using Hamiltonnian systems at a specific region on the plane in which these do not have periodic orbits. In [11] it was constructed a solution of the nonlinear Benjamin-Bona-Mahony equation using Fourier transform and Neumann series.…”

Section: Introductionmentioning

confidence: 99%

Stability in a Holling-Tanner predator-prey model like a Kolmogorov system without periodic orbits via Dulac functions

Marín¹,

Ortiz-Ortiz²,

Gutiérrez³

2018

ces

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In this work, we find Dulac functions for Kolmogorov systems which can be applied to biological models in population. With a well choose of the Dulac function h we obtain stability and a phase diagram without periodic orbits. We prove that there are not periodic orbits at the interior of the first quadrant on the plane. We also obtain a generalized Kolmogorov system and apply this to the Holling-Tanner model and we use time series to understand its behaviour.

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Solutions for the combined sinh-cosh-Gordon equation

Cited by 4 publications

References 0 publications

A Generalization of the Modified Liouville Equation

A Generalization of the Modified Liouville Equation

New exact solutions of the combined and double combined sinh-cosh-Gordon equations via modified Kudryashov method

Stability in a Holling-Tanner predator-prey model like a Kolmogorov system without periodic orbits via Dulac functions

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