Skip to main content
×
×
Home
The Direct Method in Soliton Theory
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 802
  • Cited by
    This (lowercase (translateProductType product.productType)) has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Liu, Wei and Li, Xiliang 2018. General soliton solutions to a $$\varvec{(2+1)}$$(2+1)-dimensional nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions. Nonlinear Dynamics,


    Wazwaz, Abdul-Majid 2018. A variety of negative-order integrable KdV equations of higher orders. Waves in Random and Complex Media, p. 1.


    Abenda, Simonetta and Grinevich, Petr G. 2018. Rational Degenerations of $${{\mathtt{M}}}$$M-Curves, Totally Positive Grassmannians and KP2-Solitons. Communications in Mathematical Physics,


    Wu, Pinxia Zhang, Yufeng Muhammad, Iqbal and Yin, Qiqi 2018. Lump, periodic lump and interaction lump stripe solutions to the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation. Modern Physics Letters B, Vol. 32, Issue. 07, p. 1850106.


    Iwao, Shinsuke and Nagai, Hidetomo 2018. The discrete Toda equation revisited: dual β-Grothendieck polynomials, ultradiscretization, and static solitons. Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue. 13, p. 134002.


    Huang, Li-Li Qiao, Zhi-Jun and Chen, Yong 2018. Soliton–cnoidal interactional wave solutions for the reduced Maxwell–Bloch equations. Chinese Physics B, Vol. 27, Issue. 2, p. 020201.


    Wang, Yun-Hu Wang, Hui Dong, Huan-He Zhang, Hong-Sheng and Temuer, Chaolu 2018. Interaction solutions for a reduced extended $$\mathbf{(3}\varvec{+}{} \mathbf{1)}$$(3+1)-dimensional Jimbo–Miwa equation. Nonlinear Dynamics, Vol. 92, Issue. 2, p. 487.


    Hereman, Willy 2018. Encyclopedia of Complexity and Systems Science. p. 1.

    Yao, Yuqin Zhang, Juhui Lin, Runliang Liu, Xiaojun and Huang, Yehui 2018. Bilinear Identities and Hirota’s Bilinear Forms for the (γn, σk)-KP Hierarchy. Journal of Nonlinear Mathematical Physics, Vol. 25, Issue. 2, p. 309.


    Sun, Yan Tian, Bo Xie, Xi-Yang Chai, Jun and Yin, Hui-Min 2018. Rogue waves and lump solitons for a -dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics. Waves in Random and Complex Media, Vol. 28, Issue. 3, p. 544.


    Sun, Jianqing Hu, Xingbiao and Zhang, Yingnan 2018. A semi-discrete modified KdV equation. Journal of Mathematical Physics, Vol. 59, Issue. 4, p. 043505.


    Maji, Tapas Kumar Ghorui, Malay Kumar and Chatterjee, Prasanta 2018. Advanced Computational and Communication Paradigms. Vol. 706, Issue. , p. 505.

    Chen, Shou-Ting and Ma, Wen-Xiu 2018. Lump solutions to a generalized Bogoyavlensky-Konopelchenko equation. Frontiers of Mathematics in China,


    Gegenhasi Li, Ya-Qian and Zhang, Duo-Duo 2018. Self-Consistent Sources Extensions of Modified Differential-Difference KP Equation. Communications in Theoretical Physics, Vol. 69, Issue. 4, p. 357.


    Chang, Xiangke He, Yi Hu, Xingbiao Li, Shihao Tam, Hon-wah and Zhang, Yingnan 2018. Coupled modified KdV equations, skew orthogonal polynomials, convergence acceleration algorithms and Laurent property. Science China Mathematics, Vol. 61, Issue. 6, p. 1063.


    Fang, Chun-Mei Tian, Shou-Fu Feng, Yang and Dai, Jin-Hua 2018. On the integrability and Riemann theta functions periodic wave solutions of the Benjamin Ono equation. Nonlinear Dynamics, Vol. 92, Issue. 2, p. 235.


    Chang, Jen-Hsu 2018. Soliton interaction in the modified Kadomtsev–Petviashvili-(II) equation. Applicable Analysis, p. 1.


    Xie, Xi-Yang and Meng, Gao-Qing 2018. Dark-soliton collisions for a coupled AB system in the geophysical fluids or nonlinear optics. Modern Physics Letters B, Vol. 32, Issue. 04, p. 1850039.


    Li, Li and Yu, Fajun 2018. Optical discrete rogue wave solutions and numerical simulation for a coupled Ablowitz–Ladik equation with variable coefficients. Nonlinear Dynamics, Vol. 91, Issue. 3, p. 1993.


    Zuo, Da-Wei and Jia, Hui-Xian 2018. Multi-soliton solutions of the generalized variable-coefficient Bogoyavlenskii equation. Waves in Random and Complex Media, p. 1.


    ×
  • Export citation
  • Recommend to librarian
  • Recommend this book

    Email your librarian or administrator to recommend adding this book to your organisation's collection.

    The Direct Method in Soliton Theory
    • Online ISBN: 9780511543043
    • Book DOI: https://doi.org/10.1017/CBO9780511543043
    Please enter your name
    Please enter a valid email address
    Who would you like to send this to *
    ×
  • Buy the print book

Book description

The bilinear, or Hirota's direct, method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the heavy machinery of the inverse scattering transform and was successfully used to construct the multisoliton solutions of many new equations. In the 1980s the deeper significance of the tools used in this method - Hirota derivatives and the bilinear form - came to be understood as a key ingredient in Sato's theory and the connections with affine Lie algebras. The main part of this book concerns the more modern version of the method in which solutions are expressed in the form of determinants and pfaffians. While maintaining the original philosophy of using relatively simple mathematics, it has, nevertheless, been influenced by the deeper understanding that came out of the work of the Kyoto school. The book will be essential for all those working in soliton theory.

Reviews

'Overall, the book under review is a concise and essentially self-contained book, written by one of the leading researchers associated with the development of soliton theory … provides an interesting insight into the development of a straight forward method for obtaining exact solutions for wide classes of nonlinear equations.'

Peter Clarkson - University of Kent

' … a nice example of a mathematical writing that can be read at nearly normal pace, which is extremely rare nowadays.'

Source: Zentralblatt MATH

Refine List
Actions for selected content:
Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Send to Kindle
  • Send to Dropbox
  • Send to Google Drive
  • Send content to

    To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to .

    To send content items to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

    Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

    Find out more about the Kindle Personal Document Service.

    Please be advised that item(s) you selected are not available.
    You are about to send
    ×

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 456 *
Loading metrics...

Book summary page views

Total views: 806 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 25th May 2018. This data will be updated every 24 hours.