Existence of second order solitary solutions to Riccati differential equations coupled with a multiplicative term

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

doi:10.1093/imamat/hxw050

Cited by 17 publications

(16 citation statements)

References 31 publications

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“…Condition (49) has also been observed in autonomous Riccati systems that admit solitary solutions [17].…”

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

confidence: 83%

“…; j n times. The form (16) together with (17) yields that perfect even solitons (7) can be rewritten without mixed products M a 0 M a k 1 Á Á Á M a k j :…”

Section: Canonical Form Of Perfect Solitonsmentioning

confidence: 99%

“…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%

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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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“…Condition (49) has also been observed in autonomous Riccati systems that admit solitary solutions [17].…”

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

confidence: 83%

“…; j n times. The form (16) together with (17) yields that perfect even solitons (7) can be rewritten without mixed products M a 0 M a k 1 Á Á Á M a k j :…”

Section: Canonical Form Of Perfect Solitonsmentioning

confidence: 99%

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

confidence: 99%

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An Analytical Scheme for the Analysis of Multi-Hump Solitons

Navickas

Telksnys

Timofejeva

et al. 2019

Advs. Complex Syst.

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“…4.2.1. Computation of parameter η. Coefficients p j , q j ; j = 1, 2, 3 are computed using (14) and (40). Note that to satisfy Theorem 3.1, η must also satisfy Corollary 2.…”

Section: Transformation Of (3)mentioning

confidence: 99%

“…It has already been demonstrated that in the case a 4 = b 4 = 0, system (3) does admit both kink and bright/dark solitary solutions [14,16]. The aim of this paper is to construct kink solitary solutions to (3) when parameters a 4 , b 4 are nonzero.…”

mentioning

confidence: 99%

Kink solitary solutions to a hepatitis C evolution model

Telksnys¹,

Navickas²,

Sanjuán³

et al. 2017

Discrete &Amp; Continuous Dynamical Systems - B

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The standard nonlinear hepatitis C evolution model described in (Reluga et al. 2009) is considered in this paper. The generalized differential operator technique is used to construct analytical kink solitary solutions to the governing equations coupled with multiplicative and diffusive terms. Conditions for the existence of kink solitary solutions are derived. It appears that kink solitary solutions are either in a linear or in a hyperbolic relationship. Thus, a large perturbation in the population of hepatitis infected cells does not necessarily lead to a large change in uninfected cells. Computational experiments are used to illustrate the evolution of transient solitary solutions in the hepatitis C model.

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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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Existence of second order solitary solutions to Riccati differential equations coupled with a multiplicative term

Cited by 17 publications

References 31 publications

An Analytical Scheme for the Analysis of Multi-Hump Solitons

An Analytical Scheme for the Analysis of Multi-Hump Solitons

Kink solitary solutions to a hepatitis C evolution model

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

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