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Volume 3, Issue 4
Hirota-type Equations, Soliton Solutions, Backlund Transformations and Conservation Laws

Hu Xingbiao

J. Part. Diff. Eq.,3(1990),pp.87-95

Published online: 1990-03

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  • Abstract
In this paper, first a class of Hirota-type equations Σ^l_{k=1}H_k(D_x,D_t,D_y)[F_k(D_x,D_t,D_y)f • f] • [G_k(D_x,D_t,D_y)f • f] = 0 are considered. By imposing certain conditions on F_k,G_k and H_k, we show that the abovementioned equation possesses one-soliton solution. Secondly we present a new integrable equation which is an extention of Novikov-Veselov equation and Ito equation. We obtain a Băcklund transformation (BT) of this equation. Finally we consider a generalized equation of Ramani and Sawada-Kotera, and obtain its BT. Starting with the BT an infinite number of conservation laws are derived.
  • Keywords

Soliton B&#259cklund transformation Conservation law

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COPYRIGHT: © Global Science Press

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@Article{JPDE-3-87, author = {Hu Xingbiao}, title = {Hirota-type Equations, Soliton Solutions, Backlund Transformations and Conservation Laws}, journal = {Journal of Partial Differential Equations}, year = {1990}, volume = {3}, number = {4}, pages = {87--95}, abstract = { In this paper, first a class of Hirota-type equations Σ^l_{k=1}H_k(D_x,D_t,D_y)[F_k(D_x,D_t,D_y)f • f] • [G_k(D_x,D_t,D_y)f • f] = 0 are considered. By imposing certain conditions on F_k,G_k and H_k, we show that the abovementioned equation possesses one-soliton solution. Secondly we present a new integrable equation which is an extention of Novikov-Veselov equation and Ito equation. We obtain a Băcklund transformation (BT) of this equation. Finally we consider a generalized equation of Ramani and Sawada-Kotera, and obtain its BT. Starting with the BT an infinite number of conservation laws are derived.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5815.html} }
TY - JOUR T1 - Hirota-type Equations, Soliton Solutions, Backlund Transformations and Conservation Laws AU - Hu Xingbiao JO - Journal of Partial Differential Equations VL - 4 SP - 87 EP - 95 PY - 1990 DA - 1990/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5815.html KW - Soliton KW - Băcklund transformation KW - Conservation law AB - In this paper, first a class of Hirota-type equations Σ^l_{k=1}H_k(D_x,D_t,D_y)[F_k(D_x,D_t,D_y)f • f] • [G_k(D_x,D_t,D_y)f • f] = 0 are considered. By imposing certain conditions on F_k,G_k and H_k, we show that the abovementioned equation possesses one-soliton solution. Secondly we present a new integrable equation which is an extention of Novikov-Veselov equation and Ito equation. We obtain a Băcklund transformation (BT) of this equation. Finally we consider a generalized equation of Ramani and Sawada-Kotera, and obtain its BT. Starting with the BT an infinite number of conservation laws are derived.
Hu Xingbiao. (1970). Hirota-type Equations, Soliton Solutions, Backlund Transformations and Conservation Laws. Journal of Partial Differential Equations. 3 (4). 87-95. doi:
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