Double reduction of a nonlinear (2+1) wave equation via conservation laws

作者：Bokhari Ashfaque H; Al Dweik Ahmad Y; Kara A H^*; Mahomed F M; Zaman F D

来源：Communications in Nonlinear Science & Numerical Simulation, 2011, 16(3): 1244-1253.

DOI：10.1016/j.cnsns.2010.07.007

• Partial Lagrangians
• Partial Noether operators
• Conservation laws
• Generalized double reduction
• Nonlinear (2+1) wave equation

Conservation laws of a nonlinear (2+1) wave equation u(tt) = (f(u)u(x))(x) + (g(u)u(y))(y) involving arbitrary functions of the dependent variable are obtained, by writing the equation in the partial Euler-Lagrange form. Noether-type operators associated with the partial Lagrangian are obtained for all possible cases of the arbitrary functions. If either of f(u) or g(u) is an arbitrary nonconstant function, we show that there are an infinite number of conservation laws. If both f(u) and g(u) are arbitrary nonconstant functions, it is shown that there exist infinite number of conservation laws when f'(u) and g'(u) are linearly dependent, otherwise there are eight conservation laws. Finally, we apply the generalized double reduction theorem to a nonlinear (2+1) wave equation when f'(u) and g'(u) are linearly independent.

• 出版日期2011-3
• 单位中国石油大学（北京）