Conservation laws for third-order variant Boussinesq system

✍ Scribed by R. Naz; F.M. Mahomed; T. Hayat

• Book ID: 104000884
• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 233 KB
• Volume: 23
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2010.04.003

✦ Synopsis

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 fourthorder 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.