Rocky Mountain Journal of Mathematics

Solitary wave, breather wave and rogue wave solutions of an inhomogeneous fifth-order nonlinear Schrodinger equation from Heisenberg ferromagnetism

Lian-Li Feng, Shou-Fu Tian, and Tian-Tian Zhang

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Abstract

In this paper, we consider an inhomogeneous fifth-order nonlinear Schrodinger equation from Heisenberg ferromagnetism, which describes the dynamics of a site-dependent Hisenberg ferromagnetic spin chain. Based on its Lax pair, we study the determinant representation of the $n$-fold Darboux transformation (DT). Furthermore, by using the $n$-fold DT, we obtain the higher-order solitary wave, breather wave and rogue wave solutions of the equation, respectively. Finally, the dynamic characteristics of these exact solutions are discussed.

Article information

Source
Rocky Mountain J. Math., Volume 49, Number 1 (2019), 29-45.

Dates
First available in Project Euclid: 10 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1552186950

Digital Object Identifier
doi:10.1216/RMJ-2019-49-1-29

Mathematical Reviews number (MathSciNet)
MR3921865

Zentralblatt MATH identifier
07036617

Subjects
Primary: 35Q15: Riemann-Hilbert problems [See also 30E25, 31A25, 31B20] 35Q51: Soliton-like equations [See also 37K40] 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]

Keywords
Fifth-order nonlinear Schrodinger equation Darboux transformation breather waves rogue waves solitary waves.

Citation

Feng, Lian-Li; Tian, Shou-Fu; Zhang, Tian-Tian. Solitary wave, breather wave and rogue wave solutions of an inhomogeneous fifth-order nonlinear Schrodinger equation from Heisenberg ferromagnetism. Rocky Mountain J. Math. 49 (2019), no. 1, 29--45. doi:10.1216/RMJ-2019-49-1-29. https://projecteuclid.org/euclid.rmjm/1552186950


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