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Shin'ichi OISHI, "An Analysis of Soliton Transmission Equations Reducible to a Certain Type of Coupled Bilinear Equations" in IEICE TRANSACTIONS on transactions,
vol. E63-E, no. 10, pp. 738-745, October 1980, doi: .
Abstract: Recent progress in the theory of nonlinear waves" has clarified that various nonlinear dispersive soliton transmission equations can be transformed into certain types of bilinear equations. In this paper, a general form of bilinear soliton transmission equations which have a 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 o ripples. As a result, 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 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. A simple application of these results to a design problem of soliton transmission lines is also noted.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e63-e_10_738/_p
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@ARTICLE{e63-e_10_738,
author={Shin'ichi OISHI, },
journal={IEICE TRANSACTIONS on transactions},
title={An Analysis of Soliton Transmission Equations Reducible to a Certain Type of Coupled Bilinear Equations},
year={1980},
volume={E63-E},
number={10},
pages={738-745},
abstract={Recent progress in the theory of nonlinear waves" has clarified that various nonlinear dispersive soliton transmission equations can be transformed into certain types of bilinear equations. In this paper, a general form of bilinear soliton transmission equations which have a 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 o ripples. As a result, 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 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. A simple application of these results to a design problem of soliton transmission lines is also noted.},
keywords={},
doi={},
ISSN={},
month={October},}
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TY - JOUR
TI - An Analysis of Soliton Transmission Equations Reducible to a Certain Type of Coupled Bilinear Equations
T2 - IEICE TRANSACTIONS on transactions
SP - 738
EP - 745
AU - Shin'ichi OISHI
PY - 1980
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E63-E
IS - 10
JA - IEICE TRANSACTIONS on transactions
Y1 - October 1980
AB - Recent progress in the theory of nonlinear waves" has clarified that various nonlinear dispersive soliton transmission equations can be transformed into certain types of bilinear equations. In this paper, a general form of bilinear soliton transmission equations which have a 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 o ripples. As a result, 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 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. A simple application of these results to a design problem of soliton transmission lines is also noted.
ER -
English
