A study of shallow water waves with Gardner's equation

E. V. Krishnan, Houria Triki, Manel Labidi, Anjan Biswas*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)


In this paper the dynamics of solitary waves governed by Gardner's equation for shallow water waves is studied. The mapping method is employed to carry out the integration of the equation. Subsequently, the perturbed Gardner equation is studied, and the fixed point of the soliton width is obtained. This fixed point is then classified. The integration of the perturbed Gardner equation is also carried out with the aid of He's semi-inverse variational principle. Finally, Gardner's equation with full nonlinearity is solved with the aid of the solitary wave ansatz method.

Original languageEnglish
Pages (from-to)497-507
Number of pages11
JournalNonlinear Dynamics
Issue number4
Publication statusPublished - Dec 2011


  • Conservation laws
  • Integrability
  • Perturbation
  • Shallow water waves
  • Solitary waves

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Electrical and Electronic Engineering
  • Applied Mathematics


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