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Dissipative Nonlinear Schrödinger Equation for Envelope Solitary Rossby Waves with Dissipation Effect in Stratified Fluids and Its Solution

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  • Yunlong Shi
  • Baoshu Yin
  • Hongwei Yang
  • Dezhou Yang
  • Zhenhua Xu

Abstract

We solve the so-called dissipative nonlinear Schrödinger equation by means of multiple scales analysis and perturbation method to describe envelope solitary Rossby waves with dissipation effect in stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency, and effect are important factors to form the envelope solitary Rossby waves. By employing trial function method, the asymptotic solution of dissipative nonlinear Schrödinger equation is derived. Based on the solution, the effect of dissipation on the evolution of envelope solitary Rossby wave is also discussed. The results show that the dissipation causes a slow decrease of amplitude of envelope solitary Rossby waves and a slow increase of width, while it has no effect on the propagation velocity. That is quite different from the KdV-type solitary waves. It is notable that dissipation has certain influence on the carrier frequency.

Suggested Citation

  • Yunlong Shi & Baoshu Yin & Hongwei Yang & Dezhou Yang & Zhenhua Xu, 2014. "Dissipative Nonlinear Schrödinger Equation for Envelope Solitary Rossby Waves with Dissipation Effect in Stratified Fluids and Its Solution," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, August.
    • Handle: RePEc:hin:jnlaaa:643652
    DOI: 10.1155/2014/643652
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    Cited by:

    1. Haoyu Dong & Changna Lu & Hongwei Yang, 2018. "The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations," Mathematics, MDPI, vol. 6(10), pages 1-17, October.
    2. Yin, Xiao-Jun & Yang, Lian-Gui & Liu, Quan-Sheng & Su, Jin-Mei & Wu, Guo-rong, 2018. "Structure of equatorial envelope Rossby solitary waves with complete Coriolis force and the external source," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 68-74.
    3. Seadawy, Aly R. & Rizvi, Syed T.R. & Ahmed, Sarfaraz, 2022. "Weierstrass and Jacobi elliptic, bell and kink type, lumps, Ma and Kuznetsov breathers with rogue wave solutions to the dissipative nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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