Breathers and compound solitons in the system of acoustic phonons

Smagin, V. V.; Tankeyev, A. P.; Borich, M. A.

doi:10.1134/s0031918x09110015

Cited by 11 publications

(5 citation statements)

References 9 publications

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“…A comment is in order here. Unlike the superposed solution (102), Smagin, Tankeyev and Borich [17] obtained a periodic solution of the repulsive MKdV Eq. ( 103) which is a product of two periodic kink solutions, i.e.…”

Section: Remarkmentioning

confidence: 99%

Novel Superposed Kink and Pulse Solutions for $ϕ^4$, MKdV, NLS and Other Nonlinear Equations

Khare¹,

Saxena²

2022

Preprint

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We show that a number of nonlinear equations including symmetric as well as asymmetric φ 4 , modified Korteweg de Vries (MKdV), mixed KdV-MKdV, nonlinear Schrödinger (NLS), quadratic-cubic NLS as well as higher order neutral scalar field theories, higher order KdV-MKdV and higher order quadratic-cubic NLS admit superposed periodic kink and pulse solutions and some of them also admit superposed hyperbolic kink solutions.

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Section: Remarkmentioning

confidence: 99%

Novel Superposed Kink and Pulse Solutions for $ϕ^4$, MKdV, NLS and Other Nonlinear Equations

Khare¹,

Saxena²

2022

Preprint

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“…However, only one hyperbolic superposed solution was obtained by us in some of these models as the difference of two kink solutions. In fact, even before us a number of previous researchers [2,3,4,5,6,7] had obtained such a superposed kink solution in a variety of physical models. However, to the best of our knowledge, to date no one has been able to obtain solutions which can be re-expressed either as the sum of two (hyperbolic) kink solutions or the sum or difference of two pulse solutions.…”

Section: Introductionmentioning

confidence: 99%

Superposed Hyperbolic Kink and Pulse Solutions of Coupled $ϕ^4$, NLS and MKdV Equations

Khare¹,

Saxena²

2022

Preprint

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“…Several years ago, in a largely unnoticed paper, Tankeyev, Smagin, Borich, and Zhuravlev [8,9] obtained a novel solution that could be re-expressed as a superposition of a kink and an antikink solution. Their work was inspired by the earlier work of [10].…”

Section: Introductionmentioning

confidence: 99%

Superposed periodic kink and pulse solutions of coupled nonlinear equations

Khare¹,

Banerjee²,

Saxena³

2023

Preprint

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We obtain novel periodic solutions in terms of Jacobi elliptic functions of a coupled φ 4 model as well as a coupled nonlinear Schrödinger equation (NLS) model which can be re-expressed as a linear superposition of a periodic kink and antikink, or two periodic kinks or two periodic pulse solutions. These results demonstrate that the notion of the superposed solutions extends to the coupled nonlinear equations as well.

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Breathers and compound solitons in the system of acoustic phonons

Cited by 11 publications

References 9 publications

Novel Superposed Kink and Pulse Solutions for $ϕ^4$, MKdV, NLS and Other Nonlinear Equations

Novel Superposed Kink and Pulse Solutions for $ϕ^4$, MKdV, NLS and Other Nonlinear Equations

Superposed Hyperbolic Kink and Pulse Solutions of Coupled $ϕ^4$, NLS and MKdV Equations

Superposed periodic kink and pulse solutions of coupled nonlinear equations

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