Conservation laws for third-order variant Boussinesq system

• Published in: Applied mathematics letters 2010-08, Vol.23 (8), p.883-886
• Main Authors: Naz, R., Mahomed, F.M., Hayat, T.
• Format: Article
• Language: English
• Subjects: Boussinesq equations; Boussinesq system; Conservation laws; Exact sciences and technology; Lagrangian; Mathematical analysis; Mathematical models; Mathematics; Noether; Nonlinear algebraic and transcendental equations; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations; Partial differential equations, boundary value problems; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Sciences and techniques of general use; Transformations
• ISSN: 0893-9659; 1873-5452
• DOI: 10.1016/j.aml.2010.04.003

The conservation laws for the variant Boussinesq system are derived by an interesting method of increasing the order of partial differential equations. The variant Boussinesq system is a third-order system of two partial differential equations. The transformations u → U x , v → V x are used to convert the variant Boussinesq system to a fourth order system in U , V variables. It is interesting that a standard Lagrangian exists for the fourth-order system. Noether’s approach is then used to derive the conservation laws. Finally, the conservation laws are expressed in the variables u , v and they constitute the conservation laws for the third-order variant Boussinesq system. Infinitely many nonlocal conserved quantities are found for the variant Boussinesq system.