46 citations · 235 across the 24 of their papers we have counts for
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Conservation laws and exact solutions of a nonlinear acoustics equation by classical symmetry reduction
Almudena del Pilar Márquez, Elena Recio, María Luz Gandarias
Symmetries and conservation laws are studied for a generalized Westervelt equation which is a nonlinear partial differential equation modelling the propagation of sound waves in a…
Symmetry analysis and hidden variational structure of Westervelt's equation in nonlinear acoustics
Stephen C. Anco, Almudena P. Marquez, Tamara M. Garrido +1
Westervelt's equation is a nonlinear wave equation that is widely used to model the propagation of sound waves in a compressible medium, with one important application being ultra-…
Conservation laws, symmetries, and line solitons of a Kawahara-KP equation
Almudena P. Marquez, Maria L. Gandarias, Stephen C. Anco
A generalization of the KP equation involving higher-order dispersion is studied. This equation appears in several physical applications. As new results, the Lie point symmetries a…
Conservation laws and variational structure of damped nonlinear wave equations
Stephen C. Anco, Almudena P. Marquez, Tamara M. Garrido +1
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations…
Symmetries, conservation laws, and generalized travelling waves for a forced Ostrovsky equation
Stephen C. Anco, Maria Gandarias
Ostrovsky's equation with time- and space- dependent forcing is studied. This equation is model for long waves in a rotating fluid with a non-constant depth (topography). A classif…
Nonlinearly dispersive KP equations with new compacton solutions
Stephen C. Anco, Maria Gandarias
A complete classification of compacton solutions is carried out for a generalization of the Kadomtsev-Petviashvili (KP) equation involving nonlinear dispersion in two and higher sp…
Symmetry multi-reduction method for partial differential equations with conservation laws
Stephen C. Anco, Mariluz Gandarias
For partial differential equations (PDEs) that have independent variables and a symmetry algebra of dimension at least , an explicit algorithmic method is presented f…
Line-solitons, line-shocks, and conservation laws of a universal KP-like equation in 2+1 dimensions
Stephen C. Anco, M. L. Gandarias, Elena Recio
A universal KP-like equation in 2+1 dimensions, which models general nonlinear wave phenomena exhibiting p-power nonlinearity, dispersion, and small transversality, is studied. Spe…
Conservation laws and line soliton solutions of a family of modified KP equations
Stephen C. Anco, M. L. Gandarias, Elena Recio
A family of modified Kadomtsev-Petviashvili equations (mKP) in 2+1 dimensions is studied. This family includes the integrable mKP equation when the coefficients of the nonlinear te…
Global versus local superintegrability of nonlinear oscillators
Stephen C. Anco, Angel Ballesteros, Maria Luz Gandarias
Liouville (super)integrability of a Hamiltonian system of differential equations is based on the existence of globally well-defined constants of the motion, while Lie point symmetr…
Conservation laws, symmetries, and line soliton solutions of generalized KP and Boussinesq equations with p-power nonlinearities in two dimensions
S. C. Anco, M. L. Gandarias, E. Recio
Nonlinear generalizations of integrable equations in one dimension, such as the KdV and Boussinesq equations with -power nonlinearities, arise in many physical applications and…
Conservation laws and symmetries of time-dependent generalized KdV equations
Stephen Anco, Maria Rosa, Maria Gandarias
A complete classification of low-order conservation laws is obtained for time-dependent generalized Korteweg-de Vries equations. Through the Hamiltonian structure of these equation…
Conservation laws and symmetries of a generalized Kawahara equation
Maria Luz Gandarias, Maria Rosa, Elena Recio +1
The generalized Kawahara equation appears in many physical applications. A complete classification of low-order conservation laws an…
Nonlocal symmetries of Riccati and Abel chains and their similarity reductions
M. S. Bruzon, M. L. Gandarias, M. Senthilvelan
We study nonlocal symmetries and their similarity reductions of Riccati and Abel chains. Our results show that all the equations in Riccati chain share the same form of nonlocal sy…
Classical and nonclassical symmetries of a generalized Boussinesq equation
Maria Luz Gandarias, M. S. Bruzón
We apply the Lie-group formalism and the nonclassical method due to Bluman and Cole to deduce symmetries of the generalized Boussinesq equation, which has the classical Boussinesq…