Solitons of the Nonlinear Self-Dual Network with Saturable Property

Noguchi, Akira; Watanabe, Hideaki; Sakai, Kiyoshi

doi:10.1143/jpsj.45.2009

Cited by 6 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The infinitely many conservation laws of equation (1.1) with σ = 1 were given [55,56]. The IST was used to find some shock wave and hole-type soliton solutions with non-zero asymptotic values of equation (1 Equation (1.1) with σ = 1 and saturable nonlinearity was also discussed by the IST to find four types of solitons with non-zero asymptotic values [58]. The Darboux transform (DT) of the discrete Ablowitz-Ladik spectral problem could reduce to one of equation (1.1) [59].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear self-dual network equations: modulation instability, interactions of higher-order discrete vector rational solitons and dynamical behaviours

2020

View full text Add to dashboard Cite

The nonlinear self-dual network equations that describe the propagations of electrical signals in nonlinear LC self-dual circuits are explored. We firstly analyse the modulation instability of the constant amplitude waves. Secondly, a novel generalized perturbation ( M , N − M )-fold Darboux transform (DT) is proposed for the lattice system by means of the Taylor expansion and a parameter limit procedure. Thirdly, the obtained perturbation (1, N − 1)-fold DT is used to find its new higher-order rational solitons (RSs) in terms of determinants. These higher-order RSs differ from those known results in terms of hyperbolic functions. The abundant wave structures of the first-, second-, third- and fourth-order RSs are exhibited in detail. Their dynamical behaviours and stabilities are numerically simulated. These results may be useful for understanding the wave propagations of electrical signals.

show abstract

Section: Introductionmentioning

confidence: 99%

Nonlinear self-dual network equations: modulation instability, interactions of higher-order discrete vector rational solitons and dynamical behaviours

2020

View full text Add to dashboard Cite

show abstract

“…(4) has been explored extensively in works [14,15]. As far as we could verify, relatively less work is being performed for the symbolic computation of exact solutions to fractional-type DDEs while there has been a considerable amount of work done in finding exact solutions to polynomial DDEs.…”

Section: Introductionmentioning

confidence: 99%

Construction of exact solutions for fractional-type difference-differential equations via symbolic computation

Aslan

2013

Computers & Fluids

View full text Add to dashboard Cite

a b s t r a c tThis paper deals with fractional-type difference-differential equations by means of the extended simplest equation method. First, an equation related to the discrete KdV equation is considered. Second, a system related to the well-known self-dual network equations through a real discrete Miura transformation is analyzed. As a consequence, three types of exact solutions (with the aid of symbolic computation) emerged; hyperbolic, trigonometric and rational which have not been reported before. Our results could be used as a starting point for numerical procedures as well.

show abstract

“…The first class of equations includes those of the forṁ u m = (u m−1 − u m+1 )R(u m )/(u m−1 + u m )(u m + u m+1 ), (4) R(u m ) = αu 4 m + βu 2 m + γ.…”

Section: §1 Introductionmentioning

confidence: 99%

Solutions for a System of Difference-Differential Equations Related to the Self-Dual Network Equation

Narita¹

2001

Progress of Theoretical Physics

View full text Add to dashboard Cite

We propose a system of difference-differential equations related to the self-dual network equation. By utilizing a Bäcklund transformation equation for the Toda lattice, we derive its N -soliton solution under nonvanishing boundary conditions at infinity. We present explicit expressions of four types of its 1-soliton solutions and examine them. Next, we present new formulas for finding rational solutions, and using them, we determine and analyze four types of rational solutions for these equations. Finally, we derive their elliptic function solution.

show abstract

Solitons of the Nonlinear Self-Dual Network with Saturable Property

Cited by 6 publications

References 9 publications

Nonlinear self-dual network equations: modulation instability, interactions of higher-order discrete vector rational solitons and dynamical behaviours

Nonlinear self-dual network equations: modulation instability, interactions of higher-order discrete vector rational solitons and dynamical behaviours

Construction of exact solutions for fractional-type difference-differential equations via symbolic computation

Solutions for a System of Difference-Differential Equations Related to the Self-Dual Network Equation

Contact Info

Product

Resources

About