ANALYSIS OF SOLITON TRANSMISSION EQUATIONS REDUCIBLE TO A CERTAIN TYPE OF COUPLED BILINEAR EQUATIONS.

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Abstract

A general form of bilinear soliton transmission equation which has the form of simultaneous equations for two dependent variables is presented. Then, a method is presented for constructing their generalized soliton solutions, which are solutions expressing solitons in a background of ripples. It turns out that if these bilinear soliton transmission equations have N-soliton solutions, they also have the generalized soliton solutions. Moreover, taking the modified Korteweg-de Vries equation as a typical example of the soliton transmission equations which are treated in this paper, it is also shown that its initial value problem can be solved using its generalized soliton solution. Since the results for the modified Korteweg-de Vries equation can be easily extended to all soliton transmission equations which can be transformed into a certain type of coupled bilinear equations and whose N-soliton solutions can be written by determinants, it also turns out that transmission characteristics of a wide class of nonlinear dispersive transmission equations reducible to coupled bilinear equations can be clarified by making use of their generalized soliton solutions.

Original languageEnglish
Pages (from-to)738-745
Number of pages8
JournalTransactions of the Institute of Electronics and Communication Engineers of Japan. Section E
VolumeE63
Issue number10
Publication statusPublished - 1980 Oct
Externally publishedYes

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Solitons
Korteweg-de Vries equation
Initial value problems
Wave transmission

ASJC Scopus subject areas

  • Engineering(all)

Cite this

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title = "ANALYSIS OF SOLITON TRANSMISSION EQUATIONS REDUCIBLE TO A CERTAIN TYPE OF COUPLED BILINEAR EQUATIONS.",
abstract = "A general form of bilinear soliton transmission equation which has the form of simultaneous equations for two dependent variables is presented. Then, a method is presented for constructing their generalized soliton solutions, which are solutions expressing solitons in a background of ripples. It turns out that if these bilinear soliton transmission equations have N-soliton solutions, they also have the generalized soliton solutions. Moreover, taking the modified Korteweg-de Vries equation as a typical example of the soliton transmission equations which are treated in this paper, it is also shown that its initial value problem can be solved using its generalized soliton solution. Since the results for the modified Korteweg-de Vries equation can be easily extended to all soliton transmission equations which can be transformed into a certain type of coupled bilinear equations and whose N-soliton solutions can be written by determinants, it also turns out that transmission characteristics of a wide class of nonlinear dispersive transmission equations reducible to coupled bilinear equations can be clarified by making use of their generalized soliton solutions.",
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T1 - ANALYSIS OF SOLITON TRANSMISSION EQUATIONS REDUCIBLE TO A CERTAIN TYPE OF COUPLED BILINEAR EQUATIONS.

AU - Oishi, Shinichi

PY - 1980/10

Y1 - 1980/10

N2 - A general form of bilinear soliton transmission equation which has the form of simultaneous equations for two dependent variables is presented. Then, a method is presented for constructing their generalized soliton solutions, which are solutions expressing solitons in a background of ripples. It turns out that if these bilinear soliton transmission equations have N-soliton solutions, they also have the generalized soliton solutions. Moreover, taking the modified Korteweg-de Vries equation as a typical example of the soliton transmission equations which are treated in this paper, it is also shown that its initial value problem can be solved using its generalized soliton solution. Since the results for the modified Korteweg-de Vries equation can be easily extended to all soliton transmission equations which can be transformed into a certain type of coupled bilinear equations and whose N-soliton solutions can be written by determinants, it also turns out that transmission characteristics of a wide class of nonlinear dispersive transmission equations reducible to coupled bilinear equations can be clarified by making use of their generalized soliton solutions.

AB - A general form of bilinear soliton transmission equation which has the form of simultaneous equations for two dependent variables is presented. Then, a method is presented for constructing their generalized soliton solutions, which are solutions expressing solitons in a background of ripples. It turns out that if these bilinear soliton transmission equations have N-soliton solutions, they also have the generalized soliton solutions. Moreover, taking the modified Korteweg-de Vries equation as a typical example of the soliton transmission equations which are treated in this paper, it is also shown that its initial value problem can be solved using its generalized soliton solution. Since the results for the modified Korteweg-de Vries equation can be easily extended to all soliton transmission equations which can be transformed into a certain type of coupled bilinear equations and whose N-soliton solutions can be written by determinants, it also turns out that transmission characteristics of a wide class of nonlinear dispersive transmission equations reducible to coupled bilinear equations can be clarified by making use of their generalized soliton solutions.

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