Nonlinear Dynamics

, Volume 71, Issue 1–2, pp 1–12 | Cite as

Similarity reductions and exact solutions of generalized Bretherton equation with time-dependent coefficients

  • R. K. Gupta
  • Anupma Bansal
Original Paper


In this paper, we apply Lie-group formalism to the generalized Bretherton equation with variable coefficients u tt +α(t)u xx +β(t)u xxxx +δ(t)u m +θ(t)u n =0, to investigate the symmetries. We derive the infinitesimals and the admissible forms of the coefficients that admit the classical symmetry group. The ordinary differential equations deduced from the optimal system of subalgebras are further studied and some exact solutions are obtained.


Generalized Bretherton equation Lie classical method Exact solutions 



The authors would like to thank the referees for their valuable suggestions and comments.


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.School of Mathematics and Computer ApplicationsThapar UniversityPatialaIndia
  2. 2.Department of MathematicsD.A.V. College for WomenFerozepur CanttIndia

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