High-Speed Transmission in Long-Haul Electrical Systems

Juárez-Campos, Beatriz; Kaikina, Elena I.; Naumkin, Pavel I.; Ruiz-Paredes, Hector F.

doi:10.1155/2018/8236942

International Journal of Differential Equations

2018

DOI: 10.1155/2018/8236942

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High-Speed Transmission in Long-Haul Electrical Systems

Beatriz Juárez-Campos

Elena I. Kaikina

Pavel I. Naumkin

et al.

Abstract: We study the equations governing the high-speed transmission in long-haul electrical systemsand F is the Fourier transformation. Our purpose in this paper is to obtain the large time asymptotics for the solutions under the nonzero mass condition ∫ 0 ( ) ̸ = 0.( ) the Fourier transform of the

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“…In [29], it was proved the existence of the self-similar solutions of the form u = t −1/3 f m (xt −1/3 ) to the reduced equation…”

mentioning

confidence: 99%

KdV type asymptotics for solutions to higher-order nonlinear Schrodinger equations

Naumkin,

Sanchez-Suarez

2020

ejde

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We consider the Cauchy problem for the higher-order nonlinear Schrodinger equation $$\displaylines{ i\partial_t u-\frac{a}{3}| \partial_x| ^3u-\frac{b}{4}\partial_x^4u =\lambda i\partial_x(| u|^2u),\quad (t,x) \in\mathbb{R}^{+}\times \mathbb{R},\cr u(0,x) =u_0(x),\quad x\in\mathbb{R}, }$$ where $a,b>0$, $| \partial_x| ^{\alpha}=\mathcal{F}^{-1}| \xi| ^{\alpha}\mathcal{F}$ and $\mathcal{F}$ is the Fourier transformation. Our purpose is to study the large time behavior of the solutions under the non-zero mass condition $\int u_0(x)\,dx\neq 0$. For more information see https://ejde.math.txstate.edu/Volumes/2020/77/abstr.html

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“…In [29], it was proved the existence of the self-similar solutions of the form u = t −1/3 f m (xt −1/3 ) to the reduced equation…”

mentioning

confidence: 99%

KdV type asymptotics for solutions to higher-order nonlinear Schrodinger equations

Naumkin,

Sanchez-Suarez

2020

ejde

Self Cite

View full text Add to dashboard Cite

show abstract

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High-Speed Transmission in Long-Haul Electrical Systems

Cited by 1 publication

References 34 publications

KdV type asymptotics for solutions to higher-order nonlinear Schrodinger equations

KdV type asymptotics for solutions to higher-order nonlinear Schrodinger equations

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