Hamiltonian Structure, Symmetries and Conservation Laws for a Generalized (2+1)-Dimensional Double Dispersion Equation

被引：3

作者：

Recio, Elena ^{[1
]}

Garrido, Tamara M. ^{[1
]}

de la Rosa, Rafael ^{[1
]}

Bruzon, Marfa S. ^{[1
]}

机构：

[1] Univ Cadiz, Dept Math, Cadiz 11510, Spain

来源：

SYMMETRY-BASEL | 2019年 / 11卷 / 08期

关键词：

Lie symmetry; conservation law; double dispersion equation; Boussinesq equation; CAUCHY-PROBLEM;

D O I：

10.3390/sym11081031

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

This paper considers a generalized double dispersion equation depending on a nonlinear function f(u) and four arbitrary parameters. This equation describes nonlinear dispersive waves in 2 + 1 dimensions and admits a Lagrangian formulation when it is expressed in terms of a potential variable. In this case, the associated Hamiltonian structure is obtained. We classify all of the Lie symmetries (point and contact) and present the corresponding symmetry transformation groups. Finally, we derive the conservation laws from those symmetries that are variational, and we discuss the physical meaning of the corresponding conserved quantities.

引用

页数：13

共 19 条

[1] Conservation Laws, Symmetries, and Line Soliton Solutions of Generalized KP and Boussinesq Equations with p-Power Nonlinearities in Two Dimensions [J].