Nonlinear periodic waves solutions of the nonlinear self-dual network equations

Laptev, Denis V.; Bogdan, M. M.

doi:10.1063/1.4870649

Cited by 11 publications

(13 citation statements)

References 19 publications

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“…∂Eb/∂N=ħω'=ħ(ω-kV). (19) The models of the 1D ideal anharmonic crystal and equivalent nonlinear transmission line which have been proposed by Hirota were generalized by adding the terms corresponding to the dissipation processes and the action of the external forces [30]. The equation for the generalized 1D Hirota lattice model has the form:…”

Section: The Hamiltonian Dynamics Of the Dbs And Shock Waves Of The Hmentioning

confidence: 99%

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Dynamics of discrete breathers in the integrable model of the 1D crystal

Laptev¹

2014

LoM

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In the frame of the exactly integrable model of the 1D crystal-Hirota lattice model-the dynamics and interaction of the discrete breathers has been considered. These high-frequency localized nonlinear excitations elastically interact with each other and with such excitations as shock and linear waves. Using the nonlinear superposition formula the pair collision processes of the excitations are analytically described and explicit expressions for center-of-mass shifts of shock waves (kinks) and breathers, and phase shifts of oscillations of breathers and linear waves are discussed. The dynamics of the discrete breathers and kinks as the particle-like excitations of the Hirota lattice is described using the Hamiltonian formalism. The exact nonlinear periodic solutions describing the breathers and solitons superlattices in the Hirota lattice are analysed, and their stability boundaries are determined. The analogue of the discrete breather for the finite-size system is presented in terms of the elliptic Jacobi functions and it is shown that the excitation is detached from the branch of nonlinear homogenous antiphase oscillations in the bifurcation manner.

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Section: The Hamiltonian Dynamics Of the Dbs And Shock Waves Of The Hmentioning

confidence: 99%

“…The generalized system of the NSDN equations describing the equivalent nonlinear transmission line in dimensionless units has the form [30]:…”

Section: The Hamiltonian Dynamics Of the Dbs And Shock Waves Of The Hmentioning

confidence: 99%

Dynamics of discrete breathers in the integrable model of the 1D crystal

Laptev¹

2014

LoM

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“…In [22] the new classes of periodic solutions expressed in terms of the Jacobi elliptic functions have been obtained for the Hirota lattice model and equivalent system of NSDN equations.…”

Section: The Superlattices Of the Discrete Breathers And Shock Wavesmentioning

confidence: 99%

“…The generalized models of the 1D anharmonic crystal and equivalent nonlinear transmission line contain the terms corresponding to the dissipation processes and the action of the external forces [22]. The equation for the generalized 1D Hirota lattice model has the form:…”

Section: The 1d Hirota Lattice Modelmentioning

confidence: 99%

“…The generalized system of the NSDN equations describing the equivalent nonlinear transmission line in dimensionless units has the form [22]: (11) where C(V n ), L(I n ) are determined by equation (3), G is the conductivity of the nonideal insulator, R is the active resistance of the wires and E n (t) is the external electromotive force. In [23] the periodic vibrations that represent the symmetry-determined nonlinear normal modes have been investigated using the group-theoretical method in the LCand LCR-transmission lines.…”

Section: The 1d Hirota Lattice Modelmentioning

confidence: 99%

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The superlattices of discrete breathers in the model of the 1D crystal

Laptev¹

2016

LoM

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The dynamics of the discrete breather superlattices in the model of the 1D anharmonic Hirota lattice is considered. The analogues of the discrete breather for the finite-size system with periodic boundary conditions are presented. For the analogue of the discrete breather for the finite-size system the stability and the effect of dissipation on the dynamics are discussed. Using the exact solutions of the Hirota lattice equation in the form of discrete breather superlattices the asymptotic interaction energy between two breathers is investigated. It is shown that for the considered parameters of the solutions discrete breathers in the superlattice of type I repel, while in the superlattice of type II attract each other.

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Rational solutions for the potential nonlinear lumped self-dual network equation

Feng

Zhao

2020

Applied Mathematics Letters

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Nonlinear periodic waves solutions of the nonlinear self-dual network equations

Cited by 11 publications

References 19 publications

Dynamics of discrete breathers in the integrable model of the 1D crystal

Dynamics of discrete breathers in the integrable model of the 1D crystal

The superlattices of discrete breathers in the model of the 1D crystal

Rational solutions for the potential nonlinear lumped self-dual network equation

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