Solitary solutions to a relativistic two-body problem

Marcinkevicius, Romas; Navickas, Zenonas; Ragulskis, Minvydas; Telksnys, Tadas

doi:10.1007/s10509-016-2792-2

Cited by 14 publications

(3 citation statements)

References 28 publications

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“…Note that condition (107) results from (89) and substitution (10). Also, ρ k " ν k ; k " , in (13), (14) when (107) holds true.…”

Section: Necessary Existence Conditions For (90) In (75)mentioning

confidence: 98%

“…, . The inverse balancing technique has been successfully used to obtain necessary solution existence conditions in a variety of nonlinear ordinary and partial di erential equations [10,15,18]. Note that the inverse balancing technique does not possess the drawbacks associated with various solution construction (or direct ansatz) methods, which have attracted a signi cant amount of criticism [1,8,9,17,24].…”

Section: Necessary Homoclinic/heteroclinic Solution Existence Conditimentioning

confidence: 99%

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Homoclinic and heteroclinic solutions to a hepatitis C evolution model

et al. 2018

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Homoclinic and heteroclinic solutions to a standard hepatitis C virus (HCV) evolution model described by T. C. Reluga, H. Dahari and A. S. Perelson, (SIAM J. Appl. Math., 69 (2009), pp. 999–1023) are considered in this paper. Inverse balancing and generalized differential techniques enable derivation of necessary and sufficient existence conditions for homoclinic/heteroclinic solutions in the considered system. It is shown that homoclinic/heteroclinic solutions do appear when the considered system describes biologically significant evolution. Furthermore, it is demonstrated that the hepatitis C virus evolution model is structurally stable in the topological sense and does maintain homoclinic/heteroclinic solutions as diffusive coupling coefficients tend to zero. Computational experiments are used to illustrate the dynamics of such solutions in the hepatitis C evolution model.

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“…Note that condition (107) results from (89) and substitution (10). Also, ρ k " ν k ; k " , in (13), (14) when (107) holds true.…”

Section: Necessary Existence Conditions For (90) In (75)mentioning

confidence: 98%

Section: Necessary Homoclinic/heteroclinic Solution Existence Conditimentioning

confidence: 99%

Homoclinic and heteroclinic solutions to a hepatitis C evolution model

et al. 2018

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“…The main idea of this technique is to insert (35) into ((33), (34)) and solve the resulting algebraic equations for the parameters of the system. Such derivations have been successfully applied to a number of di®erential equations [13,17,18]. Cancelling ÀKðtÞ, moving all terms to the left-hand side of (38) and applying (23) transforms (38) into:…”

Section: Double-hump Soliton Solution To a System Of Non-autonomous Rmentioning

confidence: 99%

An Analytical Scheme for the Analysis of Multi-Hump Solitons

Navickas

Telksnys

Timofejeva

et al. 2019

Advs. Complex Syst.

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An analytical framework for the analysis of multi-hump solitons is proposed in this paper. Multi-hump solitons are defined by imposing special symmetry conditions on the classical soliton expression. Such soliton solutions have a wide range of potential applications in the field of optical communications. The proposed algebras of soliton solutions enable a new look at the propagation dynamics of complex nonlinear wave phenomena. The efficiency of the presented analytical scheme is demonstrated using a system of Riccati differential equations with diffusive and multiplicative coupling.

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Application of $$\tan (\phi (\xi )/2)$$ tan ( ϕ ( ξ ) / 2 ) -expansion method for the time-fractional Kuramoto–Sivashinsky equation

Manafian

Foroutan

2017

Opt Quant Electron

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Solitary solutions to a relativistic two-body problem

Cited by 14 publications

References 28 publications

Homoclinic and heteroclinic solutions to a hepatitis C evolution model

Homoclinic and heteroclinic solutions to a hepatitis C evolution model

An Analytical Scheme for the Analysis of Multi-Hump Solitons

Application of $$\tan (\phi (\xi )/2)$$ tan ( ϕ ( ξ ) / 2 ) -expansion method for the time-fractional Kuramoto–Sivashinsky equation

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