Solitons and Conservation Laws in Neurosciences

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

doi:10.1142/s1793524513500174

Cited by 15 publications

(4 citation statements)

References 12 publications

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“…In everyday life, human beings as well as other living beings in the universe face the expression of many nonlinear phenomena [1-3; 4; 5], which at times, are detrimental to their wellbeing. To preserve themselves against this, many researchers in mathematical physics, in their commitments to understand and explain these nonlinear and dispersive phenomena, try to design nonlinear and dispersive evolution equations [2; [6][7][8][9][10][11] that can make it possible to describe the observed phenomena. One of the major particularities of the proposed mathematical models is that they admit an infinity of solutions, the most robust of which are solitary waves or solitons.…”

Section: Introductionmentioning

confidence: 99%

Hybridization of Solitary Wave Solutions in (2+1)-dimentional Complex Ginzburg-Landau Equation

Ngantcha

Omanda²,

Tchaho³

et al. 2022

CJAST

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The reflection carried out in this manuscript concerns the construction of prototypes of hybrid solitary waves, solutions of the (2+1)-dimensional complex Ginzburg-Landau equation. The principle of construction consists in injecting into the equation to be solved an ansatz that one would like solution, and that its analytical sequence results from a combination of the analytical sequences of the classical solitary waves. Then, the constraints imposed by the resolution allow to extract exact or approximate solution. As part of this work, the solution function to be constructed from the start is made up of a combination of four analytical sequences of solitary waves of the kink and pulse type. To this end, we have obtained, using a rigorous mathematical approach, important results whose graphic exploitations have made it possible to better characterize them.

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Section: Introductionmentioning

confidence: 99%

Hybridization of Solitary Wave Solutions in (2+1)-dimentional Complex Ginzburg-Landau Equation

Ngantcha

Omanda²,

Tchaho³

et al. 2022

CJAST

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“…The theory of solitons is of great importance in various fields of applied sciences and new physics [23][24][25]. Soliton solutions play the crucial role biological sciences in the filed of neurosciences [26,27]. In the current era of science and technology, physicists, engineers and mathematicians and are mostly engaged in the area of soliton theory and their vital applications.…”

Section: Introductionmentioning

confidence: 99%

Investigation of new waves in chemical engineering

2021

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Modelling of wave motion and propagation characteristics of waves is of great significant in chemical engineering. Waves are the major source of chemical actions in various real life applications. We apply an efficacious solver to give exact traveling wave solutions of the Hirota-maccari model. This solver introduces closed-form wave structures of the solutions. The traveling wave solutions are expressed by hyperbolic function solutions. These solutions may be applicable for some real life problems in chemical engineering, biological engineering, plasma physics and etc. Some two and three dimensional graphics are plotted for certain parameter values to describe the propagation of traveling wave solutions. Finally, it is pondered that the proposed approach can also be applied to another sort of complex models.

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“…[1]), and analytical aspects of these systems have been studied recently [1,2]. Conservation laws have been found in the case of cubic and other power nonlinearities [3].…”

Section: Introductionmentioning

confidence: 99%

“…In section 3, we first present the classification of all low-order conservation laws and their multipliers. Then we examine the conserved quantities defined by these conservation laws, and we discuss their physical meaning as well as their connection to variational symmetries in the case when the semilinear system (1) has a Lagrangian formulation (3).…”

Section: Introductionmentioning

confidence: 99%