Variational approaches to conservation laws for a nonlinear evolution equation with time dependent coefficients

  • AG Johnpillai
  • CM Khalique


The conservation laws of a nonlinear evolution equation of time dependent variable coefficients of damping and dispersion is studied. The equation under consideration is not derivable from a variational principle which means that one cannot appeal to  the Noether theorem to determine the conservation laws. We utilize the new conservation theorem (N.H. Ibragimov, [8]) and the partial Lagrangian approach (A.H. Kara, F.M. Mahomed, [13]) to construct local, and infinite number of nonlocal conservation laws (due to the transformation of the dependent variable) of the underlying equation.

Quaestiones Mathematicae 34(2011), 235–245.

Author Biographies

AG Johnpillai
Department of Mathematics, Eastern University, Sri Lanka
CM Khalique
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private  Bag X2046, Mmabatho 2735, South Africa

Journal Identifiers

eISSN: 1727-933X
print ISSN: 1607-3606