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Journal of Mathematical Physics / Volume 53 / Issue 1 / ARTICLES / Methods of Mathematical Physics

J. Math. Phys. 53, 013502 (2012); http://dx.doi.org/10.1063/1.3673273 (8 pages)

Investigation on a nonisospectral fifth-order Korteweg-de Vries equation generalized from fluids

Xin Yu, Yi-Tian Gao, Zhi-Yuan Sun, and Ying Liu

Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

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(Received 23 December 2010; accepted 5 December 2011; published online 4 January 2012)

In this paper, a nonisospectral fifth-order Korteweg-de Vries equation generalized from fluids is investigated. With symbolic computation, such equation is transformed into its bilinear form through a proposed dependent variable transformation with one more parameter than those in the existing literature. N-soliton solutions, Bäcklund transformation, and Lax pair in the explicit forms are constructed. Based on the above results, the characteristic-line method is applied to discuss the features of the solitons for the nonisospectral problem, i.e., the controllable solitonic velocities and widths. Four types of solitonic structures with the different solitonic velocities, widths, amplitudes, and backgrounds are also illustrated.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. N -SOLITON SOLUTIONS
  3. BÄCKLUND TRANSFORMATION AND LAX PAIR
    1. Bäcklund transformation
    2. Lax pair
  4. NONISOSPECTRAL FEATURES
  5. CONCLUSIONS

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KEYWORDS and PACS

Keywords

Korteweg-de Vries equation, solitons, transforms

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3673273

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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